diff --git a/exercises/cv_submissions/cv_tutorial_kieran_oneill.ipynb b/exercises/cv_submissions/cv_tutorial_kieran_oneill.ipynb new file mode 100644 index 0000000..5fb0559 --- /dev/null +++ b/exercises/cv_submissions/cv_tutorial_kieran_oneill.ipynb @@ -0,0 +1,296 @@ +{ + "cells": [ + { + "metadata": {}, + "cell_type": "markdown", + "source": "# Continuous Variables Tutorial: The Wigner Function", + "id": "8cbdd76d93afcd27" + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": "## 1. Introduction", + "id": "4d979819b63aa545" + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": "In this tutorial, we will explore the concept of the Wigner function, a powerful tool that can be used to visualise different quantum states of a system (or a **phase space**).", + "id": "5e64faf557d9466e" + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": "## 2. Setup", + "id": "9f862eef7d82ee1b" + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": [ + "For this tutorial, we will be using several libraries to help us visualise and analyse the Wigner function. We will also be defining some constants:\n", + "- `N`: Hilbert space cutoff we will be setting this to a managable number, but the size of this number is dependent on your system, but it can be infinite.\n", + "- `PHASE_SPACE_GRID`: The phase space grid simply defines the range of values for the phase space coordinates (x and p)." + ], + "id": "13481c3592be245f" + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2026-08-10T05:51:10.396224871Z", + "start_time": "2026-08-10T05:51:09.548768709Z" + } + }, + "cell_type": "code", + "source": [ + "import matplotlib.pyplot as plt\n", + "import matplotlib.ticker as ticker\n", + "import numpy as np\n", + "import qutip as qt\n", + "\n", + "N = 20\n", + "PHASE_SPACE_GRID = np.linspace(-5, 5, 200)" + ], + "id": "cd06427a3ab8b6d6", + "outputs": [], + "execution_count": 1 + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": "## 3. Phase Space and the Wigner Function", + "id": "dd9917a6f61db7d9" + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": "### 3.1. Phase Space", + "id": "309b1cbd36f5ec83" + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": [ + "In classical physics, we often describe an oscillating system as having the properties:\n", + "- **position** ($x$)\n", + "- **momentum** ($p$)\n", + "\n", + "For example, if we take a simple demonstration of a weight on a spring, when the position ($x$) of the weight oscillates between two extremes, the momentum also changes ($p$) in response to a force (for instance, gravity).\n", + "\n", + "When plotted against time, this is shown as a cosine wave." + ], + "id": "50329e11a748bc10" + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": [ + "
\n", + " \n", + "
" + ], + "id": "ebb1c8c4107dc7cc" + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": [ + "When we want to describe where a quantum particle is and how fast it is moving, in classical physics, we would just say: \"It is at position x with momentum p.\" However, in quantum mechanics, you cannot just pin down both position and momentum at the same time because of the [Heisenberg Uncertainty principle](#41-heisenberg-uncertainty-principle-). So instead of a single point, a quantum state is more like a cloud spread out over a map where one axis is position and the other is momentum. This \"cloud\" of space is what we refer to as the **phase space**.\n", + "\n", + "We can visualise this **phase space** as a plot of position ($x$) against momentum ($p$):" + ], + "id": "4b957de4bf637ca5" + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2026-08-10T05:51:10.525597567Z", + "start_time": "2026-08-10T05:51:10.416563243Z" + } + }, + "cell_type": "code", + "source": [ + "def _hide_zero(value, _) -> str:\n", + " return \"\" if np.isclose(value, 0) else f\"{value:g}\"\n", + "\n", + "def plot_phase_space(\n", + " state: qt.Qobj | None = None,\n", + " title: str | None = None,\n", + ") -> None:\n", + " fig, axis = plt.subplots(figsize=(6, 6))\n", + "\n", + " axis.set_xlim(PHASE_SPACE_GRID[0], PHASE_SPACE_GRID[-1])\n", + " axis.set_ylim(PHASE_SPACE_GRID[0], PHASE_SPACE_GRID[-1])\n", + "\n", + " ticks = np.linspace(-5, 5, 11)\n", + " axis.set_xticks(ticks)\n", + " axis.xaxis.set_major_formatter(ticker.FuncFormatter(_hide_zero))\n", + " axis.set_yticks(ticks)\n", + " axis.yaxis.set_major_formatter(ticker.FuncFormatter(_hide_zero))\n", + "\n", + " axis.spines[\"left\"].set_position(\"zero\")\n", + " axis.spines[\"bottom\"].set_position(\"zero\")\n", + "\n", + " # hide outer frame\n", + " axis.spines[\"top\"].set_visible(False)\n", + " axis.spines[\"right\"].set_visible(False)\n", + "\n", + " # Put tick marks on the inner axes and point them inward\n", + " axis.tick_params(\n", + " axis=\"both\",\n", + " direction=\"in\",\n", + " right=False,\n", + " top=False,\n", + " which=\"both\",\n", + " )\n", + "\n", + " axis.grid(True, linestyle=\"--\", alpha=0.6)\n", + "\n", + " # add labels\n", + " axis.set_xlabel(\"x\")\n", + " axis.xaxis.set_label_coords(1.03, 0.47)\n", + " axis.set_ylabel(\"p\", rotation=0)\n", + " axis.yaxis.set_label_coords(0.53, -0.08)\n", + "\n", + " # add the phase state\n", + " if state is not None:\n", + " vmax = np.max(np.abs(state)) * 0.9\n", + " axis.contourf(\n", + " PHASE_SPACE_GRID,\n", + " PHASE_SPACE_GRID,\n", + " state,\n", + " 200,\n", + " cmap=\"RdBu_r\",\n", + " vmin=-vmax,\n", + " vmax=vmax\n", + " )\n", + "\n", + " if title is not None:\n", + " axis.set_title(title, fontsize=14, fontweight=\"bold\")\n", + "\n", + " axis.set_aspect(\"equal\", adjustable=\"box\")\n", + "\n", + " plt.tight_layout()\n", + " plt.show()\n", + "\n", + "plot_phase_space(title=\"Empty Phase Space\")" + ], + "id": "3b426275833f13af", + "outputs": [ + { + "data": { + "text/plain": [ + "
" + ], + "image/png": "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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "execution_count": 2 + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": "### 3.2. The Wigner Function", + "id": "f91a07da1585edce" + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": [ + "The Wigner function is a way to visualise the phase space. If we think of it like a weather map for quantum states: it assigns a number to every point in phase space, telling you something about how likely the particle is to be found there. The colors in our plots work like this: red and yellow areas are where the state \"likes to hang out\" (positive values), while blue areas are strange—they represent negative values, which is something you'd never see in a normal probability map. Those blue regions are a smoking gun for quantum weirdness; they're impossible in classical physics and signal that quantum interference is happening.\n", + "\n", + "For a quantum state with wavefunction $\\psi(x)$, the Wigner function is computed as:\n", + "\n", + "$$W(x, p) = \\frac{1}{\\pi \\hbar} \\int_{-\\infty}^{\\infty} \\psi^*(x + y) \\, \\psi(x - y) \\, e^{2ipy/\\hbar} \\, dy$$\n", + "\n", + "This formula takes the wavefunction at two nearby positions (x+y and x−y), multiplies them together, and performs a Fourier transform to extract the momentum information at each point in phase space.\n", + "\n", + "Even though the Wigner function can dip below zero in some places, it still behaves like a proper probability distribution overall as the total \"amount\" across the entire phase space adds up to exactly 1." + ], + "id": "5d61c65d7fdece29" + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": "#### 3.2.1. Example: The Vacuum State", + "id": "c10032dc885973a5" + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": [ + "The **vacuum state** or the \"ground\" state is the lowest-energy state of a harmonic oscillator and is usually represented as $|0\\rangle$.\n", + "\n", + "As a Wigner plot in phase space, it appears a symmetric, circular Gaussian blob centered at $(x=0, p=0)$ and is the most compact state in quantum mechanics.\n", + "\n", + "What is interesting is that you will notice that despite being the lowest state, the plot is not exactly zero, this is because the \"blob\" represents quantum fluctuations." + ], + "id": "1963210aa6692777" + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2026-08-10T05:51:10.745159819Z", + "start_time": "2026-08-10T05:51:10.529469659Z" + } + }, + "cell_type": "code", + "source": [ + "# use qutip to calculate the wigner function of vacuum space (0)\n", + "wigner_function = qt.wigner(qt.basis(N, 0), PHASE_SPACE_GRID, PHASE_SPACE_GRID)\n", + "\n", + "plot_phase_space(state=wigner_function, title=\"Wigner function W(x, p) of vacuum state |0⟩\")" + ], + "id": "3d199268ac3bfb22", + "outputs": [ + { + "data": { + "text/plain": [ + "
" + ], + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkcAAAJOCAYAAAC9TKM/AAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjExLjEsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvctoD+AAAAAlwSFlzAAAPYQAAD2EBqD+naQAA7IRJREFUeJzsnXmYFMX5x79VPTO7yy57cCywHAvL7YEKeKMCKmrUeMQ7eOJFDtGo0Wi84n0nGjXxiv5M4hENqBElHhjjGUTFC1hgYUFhhYW9l92Z6arfH31Md0/P7Mxuz+w0vJ/nmWdmqrur3+prvvO+b1UxKaUEQRAEQRAEAQDgvW0AQRAEQRBELkHiiCAIgiAIwgKJI4IgCIIgCAskjgiCIAiCICyQOCIIgiAIgrBA4oggCIIgCMICiSOCIAiCIAgLJI4IgiAIgiAsBHrbAIIgCILYGejo6EA4HM7a/kKhEPLz87O2vx0JEkcEQRAEkWE6OjrQv6AI7VCzts/Bgwdj7dq1JJC6AYkjgiAIgsgw4XAY7VDxUwxFKAsZLWEI/K3ue4TDYRJH3YDEEUEQBEFkiRB4VsQR0TPoDBEEQRAEQVggcUQQBEEQBGGBxBFBEARBEIQFEkcEQRAEQRAWSBwRBEEQBEFYIHFEEARBEARhgcQRQRAEQRCEBRJHBEEQBEEQFkgcEQRBEARBWCBxRBAEQRAEYYHEEUEQBEEQhAUSRwRBEARBEBZIHBEEQRAEQVggcUQQBEEQBGGBxBFBEARBEIQFEkcEQRAEQRAWSBwRBEEQBEFYIHFEEARBEARhgcQRQRAEQRCEBRJHBEEQBEEQFkgcEQRBEARBWCBxRBAEQRAEYYHEEUEQBEEQhAUSRwRBEARBEBZIHBEEQRAEQVggcUQQBEEQBGGBxBFBEARBEIQFEkcEQRAEQRAWSBwRBEEQBEFYIHFEEARBEARhgcQRQRAEQRCEBRJHBEEQBEEQFkgcEQRBEARBWCBxRBAEQRAEYYHEEUEQBEEQhAUSRwRBEARBEBZIHBEEQRAEQVggcUQQBEEQBGGBxBFBEDnPo48+itNOOw0vvvhij+vavn076uvrUV9f74FlBEHsiAR62wDCf9xyyy34+uuvAQAVFRW47777XNdrb2/H+eefDyEEAOC4447D6aefnjU7iR2H//3vf3j++ecxYcIEnHTSSXHLhRB44403sHjxYmzevBklJSXYb7/9cMIJJ6CgoMC27uuvv46f/OQnAIBPPvkE++yzT1baQBCEfyBxRKRNUVERnn/+efP73LlzMXbs2Lj1Xn75ZTz77LPm91/+8pdZsY8Atm3bhp/97Gfm99tuuw1VVVU5W29PqKurw3HHHYf//e9/tvIHH3wQlZWVmD9/Pvbaay+z/Mgjj0RBQQG2b9+Ol19+mcQRQRBxUFiNSJszzjgDgUBMV//97393Xe9vf/ub+bmqqgoHHnhgxm0jNNrb2/H888+br23btuV0vd0lEongqKOOMoXR9OnT8eSTT+Kss84CANTW1uLwww/HDz/8YG7Tp08fHH744QCABQsWZN1mgiByHxJHRNqUl5dj1qxZ5nerCDLYunUr/v3vf5vfzzzzzKzYRuxc/OUvf8EXX3wBAOjXrx/+9a9/4dxzz8XTTz+NfffdF4B2Lf7ud7+zbXf88ccDAL799lusWrUqmyYTBOEDKKxGdIuzzjoLCxcuBACsWrUKS5Yswd57720uf+GFFxCJRMzvhjj6/PPPceedd9rqysvLw6BBg7DvvvvimGOOQV5enus+m5ub8corr+Czzz7D1q1bUV5ejn333RcnnHACFEUBADz77LN4+eWXAQAjR47EHXfcYW7/1ltv4fHHHwcAFBcX49FHHzWXdXe7119/HU8//TQAoLS0FH/605/w/vvv4/nnn0ckEsHhhx+OE088EYwxbNu2DU8++SS+/fZbVFRU4NhjjzV/wFNl7dq1mD9/Pqqrq9He3o6KigqMGzcOhx9+OIYPHw4AuPHGG/H555/btrv22mtRVlYGADjkkEMwd+7ctM9FqvUabN26FfPnz8eyZcvQ2NiI0tJS7L333jjppJPQp0+ftNqdCKvXcsaMGSgsLDS/H3300fjkk08AaOf3j3/8IxhjAIBjjz0WiqJAVVUsWLAAV155pSf2EASxgyAJohts375dlpSUSAASgJw3b55t+bRp08xlBx54oFn+6quvmuVur6qqKrlixYq4/T3xxBOyb9++rtuMHz/eXO+qq64yy/fcc09bHY888oi5rH///rZl3d3u/vvvN5cNGjRIPvjgg5IxZrNvzpw58ptvvpFDhw61lTPG5MMPP5zyMX/mmWdkIBBwPQaMMXnZZZdJKaU88MADkx7js88+u1vnItV6pZTy4Ycfln369HFdb/DgwfLdd99Nud1SSjlnzhwJQN5www1mmRBCFhYWmvVeccUVccfLut/q6mrb8kMOOUQCkAcccEBathBEd2hqapIA5LkYLi9CZcZf52K4BCCbmpp6u+m+hDxHRLfIz8/HySefbHpUnnvuOdx7771QFAW1tbX44IMPzHWN/A8AmDx5si1JW1VV1NXV4emnn8ZXX32FmpoanHnmmbbk2meffRZz5swxv+++++4488wzUVxcjM8//xzz5893tdHwEqRLd7draGjAXXfdhfvvvx+bNm0yvTJPPPEEXnnlFUyYMAHXX389/vGPf+Ctt96ClBJXXXUVzj777JQ8KVdeeSWi0SgALbl96tSpqK+vx6pVq/DKK6+guroaAHDTTTdh5cqV+PnPf25ue+utt5qJ06NGjQKQ/rlItd6//vWvZtK2oii48MILMXXqVHzwwQd48sknUVdXh2OOOQafffaZayJ/qjQ1NaGtrc38XlJSYlvu/L5p0ybb/o4//nj85z//wccff4zNmzejvLy827YQxI7A22+/jcceewz19fWYMmUKrrrqKvTr1y/h+lu2bMGf//xnfPLJJ8jPz8eMGTNwwQUXIBgMmutEIhE8+eSTePPNN9Hc3IxRo0bhoosuwuTJk9NaJ+v0tjoj/Mt//vMf2z/zRYsWSSmlvO2228yyvLw82dDQ0GVdGzZssNW1Zs0ac9nIkSPN8ilTpshwOGzbtq6uzvxs9QBNmTLFtl6qnqN0trN6jgDIt956y1w2ZswYs7xfv36yvb1dSinl8uXLbdt8/vnnXR4fVVVlKBSSAGR+fr7ctm1b3HKrl8d5PJcsWdLlPhJtaz0XqdRbWVlpLr/66qtty44//nhz2XnnnZeyTW6eo02bNtlsue2222zbvPbaa7blb7zxhm352rVrzWWPPfZYyrYQRHfIdc/Rq6++KgOBgLzpppvk/Pnz5YEHHih333132dnZ6bp+Y2OjHDlypLzuuuvkq6++Kv/v//5Pjho1Sh599NFSCGGuN2fOHDlkyBD5l7/8RS5atEhefPHFMi8vTy5dujStdbINeY6IbnPQQQdh1KhRWLt2LQAtMXvWrFm2PJBjjz0WpaWltu1qa2vx2muvYcWKFWhsbEQ4HDbHQjJYs2YNqqqqUFtbi3Xr1pnlF198se1fCQAMGjTI24Z1k0AggBkzZpjfBw0ahNWrVwMADj74YHO8nYqKCtt21p5UieCc44ADDsC7776Ljo4ODB06FLvssgvGjh2LXXfdFYcddhj222+/tG1O51ykwrp161BbW2t+//jjj3HaaaeZ363Jz//5z3/SttdK3759bd/D4bDte2dnZ9L1R44cif79+2Pr1q347LPPemQLQfid3/zmNzj33HNx/fXXA9Ce7xUVFfjrX/+K8847L279wsJCfPPNNzav9/DhwzFjxgysWLECEydOBAD885//xLXXXotzzjkHADBr1iy8+uqreO2110zPUCrrZBsSR0S3YYxh9uzZuPnmmwEA8+fPx9y5c80BIgF7SA3Qxp657LLLoKpq0rrb29sBaKETK+mEPqSUtu/OH0+vt+vXrx84j3UAtQ53YLXbKT6c+0vE008/jTlz5uDtt9/G9u3bsXTpUixduhQAcN111+GUU07Bc889l3JYMN1zkQrNzc227++++27Cdbds2ZJyvW4UFhZi8ODBqKurc63POQL2mDFjbN+NxH4AOPTQQ3tkC0H4mbq6Onz99de4/fbbzbL+/fvjwAMPxJtvvukqjgKBgO0ZB8RC2R0dHWbZ5MmTsWTJEgghwDnHqlWrsHXrVkyZMiWtdbINiSOiR5x55pmmOGppacG5555rLhs4cCCOPPJI83tDQwMuv/xy88d42rRpOOOMM1BWVobt27fbbkBDMAwdOhSMMfP7N998gx//+McJ7bHerNYbFNA8IF5vZyWZKOluHpOVESNG4M0338TWrVuxbNky1NTUYOnSpXjsscegqipeeOEF/PKXv8S0adO6rKs75yIVnOfrqquuwp577um6rtMD2B0OPvhgvPDCCwC0bvlWvvrqK/Pz+PHj44S1McZRfn6+7ToliB0J5x+WvLy8uB7Bhrd36NChtvKhQ4eipqYm5X3dfvvtGDVqFHbffXez7B//+AfOOussjBgxAoMGDcK6devw6KOP4kc/+lFa62QbGueI6BFjx461hXNWrFhhfj7ttNNsP4A//PCDrXv/rbfeirlz5+K0006zlVvp378/Dj74YPP7fffdZ/sRFELgmWeeMb+PGDHC/FxTU2OGrDZs2IC//vWvCdvR3e2yyQMPPIDq6mr0798fM2fOxPnnn4+HHnrIFvIyHnL5+fm2bZ2DNXbnXKRSb//+/W3i7Msvv8Txxx+P0047zXwde+yx4JzHhVu7w0UXXWR+fv/997F8+XIAmvj7xz/+YS67+OKL47Y1xNFhhx1mGwKAIHYkhg8fjpKSEvNl9Q4ZGPe88/4uKChI2XN+22234dVXX8Xf/vY325/N3//+9/jss89w00034bbbbsOpp56Kq666CitXrkxrnWxDniOix5x11ln4+OOPXcutjB07FoMGDTKFx4knnoiDDjoIGzdutPU6cvLggw/ioIMOQlNTE+rr67Hnnntin332QXFxMb766its2bLFHEfp0EMPRSgUQjgcRkdHB/baay/sueee+PjjjzFixIiEIzp3d7tsct9992HevHkYNWoUKisr0a9fP3zzzTdmHk8wGDSF6oABAzBkyBBs2rQJAHDOOefggAMOQCAQwLx587DPPvt061x0Ve/++++PP/7xjzjooIPQ3NyM119/HcOHD8fUqVPBOcf69euxevVqdHR04O677+5xOGvmzJm44IIL8NhjjyESiWD//ffH9OnTsXTpUjPcdsABB+AXv/iFbbuamhrTs2QMCEkQOyIbNmxAcXGx+d1tHDmjR5oRZjbYunVr0t5qBvfffz9uvvlmLFiwAPvvv79ZXldXh1tuuQXPPfccTj75ZADAEUccgS+++AK/+93v8Le//S2ldXoD8hwRPebUU09FKBSylU2cOBFTp061lSmKgpdeegmVlZUAtBtvwYIFEEIkncZh9913x//+9z8cc8wx4JwjEonggw8+wOuvv45t27bZupaPHj0aDz/8MIqKigBo3bfffvttXHnlla7eg55ul00uv/xy7LXXXli7di3effdd/POf/zT/WY0YMQIvvPACRo8eba5/3333mf8EN23ahJdeegnPP/88amtru30uuqoXACZNmoRPPvkERx11FBhjqK+vxxtvvIGFCxfi66+/Rl5eHk4//XQcdthhnhyXP/3pT7jppptQVFSEpqYmvPzyy/juu+8QCAQwZ84cvPHGG3G5EcbwD5xzHHvssZ7YQRC5SHFxse3lJo7Gjh2LoqIiM4fR4NNPP7XNS+jGH/7wB1xzzTWYP38+jjjiCNuyhoYGCCEwbNgwW/mwYcNMIZbKOr0Bk+kkFBBEAv7973/bvCtjxoyJE0cG4XAYn3/+OTZt2oThw4djypQpEEKYuSOA1lPCGf8GtBtp2bJl2LZtG8rLyzFp0iTbvyLrel9++SVaWlqwzz77oLy8HGvWrMGSJUsAaP+eTjjhhB5vV11dbfZ0KigowHHHHWcue+edd7B58+a44xGJRPDSSy+Z602fPh2DBw92PVZu1NXVoaamBnV1dQiFQqiqqsLEiRNd85oaGxuxZMkS8wEEaJ4UI4zY3XPRVb0GW7duxZdffolt27ahtLQUQ4cOxejRo9PONzr//PPxxBNP4IYbbsCNN97ouk5HRweWLFmCLVu2oKSkBFOmTEkYups2bRo++OADTJs2Df/973/TsoUgukNzczNKSkpwLoYjlAW/RBgCf8EGNDU1uT4jncydOxdvv/02Pv74Y/Tr1w9PPfUUzj//fHz11Vdmz7PrrrsOW7duxcMPPwxA8+r/+te/xvz5813z9qLRKIYNG4YjjzwSjz/+OAKBAFatWoV99tkHl19+OX7729+mtE5vQOKIIIicJxVxlCqbN2/GkCFDIITAPffcg8svv9wbIwkiCbkujlpaWnDSSSfhww8/xNChQ/Hdd9/hwQcftHWyOemkk1BXV4f3338f69evx8iRIzFw4MC4wVxvueUWTJ8+HQDw3nvv4dxzz0V7ezsGDx6MFStW4MQTT8STTz5perFSWSfbUM4RQRA7FR999JH5MKd8I4LQ6Nu3LxYtWoS1a9eivr4eEydONNMMDG655RYzebu8vBzvvfeea12GpwnQepRWV1ejtrYWjY2NGDlyZFweUyrrZBsSRwSRRVRVxfbt2+PKCwsLPenuT3TNcccdZwt/EgQRY9SoUeZUQE4mTJhgfs7Pz09p2BBAyzftaiDZVNbJJiSOCCKLzJ8/HyeffHJc1/Gamhqa2ysJF110EQ477DDstttuvW0KQfQIBYCShf9BCiXM9AgSRwSRZUpKStDY2NjbZviKvffeG3vvvXdvm0EQxE4CdeUniF5ACNHltB0EQRBE70DiiCCyTHNzM4qKilBYWIi99toL//rXv3rbJIIgCMICiSOCyCIlJSV44oknUFdXhy1btuAnP/kJfvzjHyecoFVKiS1btqCpqQnNzc3myznjPEEQ/kBhLGsvovt4knP01ZdfojMcNnvblJaWYmhFBb7fuNGWWzFwwACUl5ejtrYWrZYpCiqGDEFZWRlWr16NTss8LpUjRqCoqAjLV6ywzWQ+uqoKwWAQKxzzrkwYPx6RSARrLBPlcc4xccIEtLa2Yl1tLTo6OpCfn4/8vDyMGTMGDQ0N2KhPhQAARYWFqKysxObNm7HFMqt3ttskpURHRwf2mDQJqqombFPt+vVmeV4o1Gtt6tOnD7744guE8vLM66C75ynTbWppbTWvg6EVFVm59ow29evXD0MGD0YoGERDQwOOOuooLFiwAL/73e8wZPDguDa1tLRgxowZcHLBBRfgt9de26v3k/M8VVVVYd26dWjfvt28BnLlfnK2afWaNeY1oChKzt1PzjZJKVFWWory8nJU69PFdPc8ZbpNJSUl+Oqrr6AEAuZ1kOlrr7ttamhoSDhYLbFz48kgkJ9++inGjR0LRVG0ShkD5xxCCNuM3umWc87BGIvLzeBcc3hZb7Jk5YqiQEqJSCSC6lWrMG7sWAQCAU9szFSbVFVF9apVmDB+PBRFSdgma3mmbU/WJiEElq9YYbsOunueMt2maDTa5XXg9bWXrE3zLr0US5YswUcffhhnS0NDA4aPGIGVK1aguLjYLM/Ly0N+fn6v3k/ONkkp466BXLmfnOXWZ4GiKDl3PznbZH0eOId86O37yVnudh1k835KpzwajaK4pATZwBgE8iI2AiGWhUEgpcCf5fqUB4Ek7HjiOSorKzN/ZKw4v3e33LjBelLOGEMgEIiz1SsbvW4TYwxlZWXmQyVRm9zKe6NNhr1u10G65ynTbUrnOvDq2kvWpi+//BLDhw1ztcWYE6y4uDjhVBi9dT85y4UQGX8WeNUmt2sgl+4nwG679XmQzjHojTYluw6ycT+lU+6ccy8bcJadrvwcAKg7f7fx5MoYWlHhRTUZh3NOtmYIP9nbm7ZeeOGFOOzww7HffvshEg7jjw89hM8++wwLX3vNdf2uxFsuQddA5vCTvX6zlSDc8OTK+H7jxjj3Zy4ihCBbM4Sf7O1NW6+99lq8/dZbmDVrFn509NHYsH49Fr/zDg4++GDX9Q0b6bh6i59sBfxlr99sJQg3PPEcNTY2YvCgQV5UlVGklGRrhvCTvb1pa2VlJf785z+nvL6RK+GH+aHpGsgcfrLXb7YShBs0QjZBEARBZIlsdbNXQF35ewIFXAmCIAiCICx4Io4GDhjgixnFGWNka4bwk71+s9X6nsv47bj6xVbAX/b6zVaCcMOTsJpfZhPnnJOtGcJP9vrNVut7LuO34+oXWwF/2es3WwnCDU+ujNraWl9k/QshyNYM4Sd7/War9T2X8dtx9YutgL/s9ZutBOGGJ+Kota3NF1n/UkqyNUP4yV6/2Wp9z2X8dlz9YivgL3v9ZitBuEE+RYIgCIIgCAvUlZ8gCIIgsoSSpelD3CdkIVLFE89RxZAhvsj6Z4yRrRnCT/b6zVbrey7jt+PqF1sBf9nrN1sJwg3PJp71A5xzsjVD+Mlev9lqfc9l/HZc/WIr4C97/WYrQbjhyZWxevVqX2T9CyHI1gzhJ3v9Zqv1PZfx23H1i62Av+z1m63ZxhghOxsvovt4Io46w2FfZP1LKcnWDOEne/1mq/U9l/HbcfWLrYC/7PWbrQThBvkUCYIgCIIgLJA4IgiCIAiCsOBJQnbliBG+SGzjnJOtGcJP9vrNVut7LuO34+oXWwF/2es3W7MNdeX3B56Io6KiIi+qyTiMMbI1Q/jJXr/Zan3PZfx2XP1iK+Ave/1mK0G44YlsXr5iBVRV9aKqjKKqKtmaIfxkr99stb7nMn47rn6xFfCXvX6zlSDc8MRz5IcumwZka+bwk71+stVP+Om4+slWwF/2+snWbJOtbvYKyCvWE3I/KEwQBEEQBJFFSBwRBEEQBEFY8EQcja6q8k3PBLI1M/jJXr/Zan3PZfx2XP1iK+Ave/1mK0G44UnOUTAY9KKarEC2Zg4/2esnW/2En46rn2wF/GWvn2zNNgzZCdlQxlHP8OQcrVi50hcJeEIIsjVD+Mlev9lqfc9l/HZc/WIr4C97/WYrQbhBPkWCIAiCIAgLnoTVCIIgCILoGurK7w/Ic0QQBEEQBGGBSSllTytpa20F5zznh2KXUkIIQbZmAD/Z6ydbm5qaMHjIENRt2oSSkpLeNicpfjqufrIV8Je9frO1oE+frOyrubkZJSUl+G1+FfJZ5v0SHVLglo4aNDU1obi4OOP729Hw5AxFIhEvqskKZGvm8JO9frLVT/jpuPrJVsBf9vrJVoJwwxNxtKamxhdZ/0IIsjVD+Mlev9lqfc9l/HZc/WIr4C97/WZrtlFY9l5E96GcI4IgCIIgCAskjgiCIAiCICx40pXfT0Owk62Zw0/2+slWP+Gn4+onWwF/2esnW7ONFvLKRld+oid40lutY/t2L2whiJ2KZcuW4Zxzz8Xoqiq8+OKLrus0Nzdj0ODB+KGujnqcEEQGyC8oyMp+jN5qv+tThXyWeenSIVVc30691bqLJ56j1tZWFBYW+qLbZltbG9maAfxkby7Y2tbWhrPPOQeFffpg7bp1Cdcz/rt48B8m4+TCcU0VP9kK+Mtev9lK2FmxYgXq6+ux6667oqysrMv1Ozo68M033yA/Px9jx45FKBSyLf/6669RV1dnKystLcXUqVNd6/ryyy9RWlqKcePG9awhPcQT32ft+vW+6ZlAtmYGP9mbC7ZeetllmDVrFg46+OCk6/mtt1pvH9dU8ZOtgL/s9ZuthEZTUxOmT5+O/fffH7/4xS8wdOhQ/PnPf064fiQSwZVXXokRI0bgoosuwnHHHYfRo0dj0aJFtvVuueUWnH322bjjjjvM19/+9re4+h577DEMHjwY559/Pk477TQceeSRaGpq8rydqULThxBElnn2ueewbNky/Pe993DDjTf2tjkEQWSRbHWzTzdwd8UVV+CHH37AunXrUFJSgr///e8488wzceCBB2K33XaLW3/79u0YNGgQ1q5di8LCQgDA1VdfjZNPPhkbNmywDVp71FFH4fHHH0+47/nz52Pu3LmYP38+jj32WADAO++8g4aGhl4b/NYTcSSlhKqq5nfGGDjnEELY3JbplhsjrFrrNsqBeNWfqFxRFNNG490rGzPVJsNW45WoTdby3mwTEH8ddPc8ZbpNqVwHXl97RvmaNWvw61//Gm+8/jqCwSCkvt9Ethj7b2lpAWPMLM/Ly0N+fn6v3k/O8wRk7lngdZus10CyNuXKM8L6PEi1rb3VJsD9WZDJa68nzwICCIfDePbZZ3H77bebYuSMM87Atddei//7v//DXXfdFbdNcXExrrjiClvZueeeizvvvBPffPMNDjjgALO8paUF77//PgYMGIAxY8YgELBLj5tuugmnnnqqKYwAYObMmV42MW08EUdqNIrqVavMG6O0tBRDKyqwqa4OjY2N5noDBwxAeXk5NmzYgNa2NrO8YsgQlJWVoaamBp3hsFleOWIEioqKUL1qle1mGF1VhWAwiBUrV9rsmDB+PCKRCNbU1JhlnHNMnDABbW1tWFdbi5bmZlSvWoX8vDyMGTMGTU1N2Lhpk7l+UWEhKisrUV9fjy319WZ5ttskpURLczOklOjs7EzYptr1683yvFCo19rUp08ftLa02K6D7p6nTLeppbXVvA6GVlRk5dqrXb8ekUgE5513Hs6fMwe77rorGhoasK2hAZ2dnVixcqVrm1paWgAA4ydMsO3vggsuwG+vvbZX7yfneaqqqoKU0nYN5Mr95GzT6jVrzGtAUZScu5+cbZJSIqALg5XV1T06T5luU0lJCdrb2mzXQaavve62qaGhwTX3ZUeiubnZ9j0vLw95eXm2slWrVqGtrQ2TJ0+2lU+ePBlffPFFyvv6+OOPwTnH6NGjbeX/+te/sG7dOmzYsAGBQACPP/44Zs2aBQDYunUrli1bhiuvvBJbtmxBdXU1hg8fjhEjRqTRSu/xpLdae1tbTv0rzJV/UNQmapO1TStXrsSUqVMxduxY7UdDStTX16O1rQ2VlZV4+KGHMG3aNJstzc3NqBg6FKtXrUJhYWFOe452lPNEbdq52lRYVIRsYPRWu7Uwe73Vrm2riSu/4YYbcKMjnP/+++/joIMOwrfffouJEyea5RdeeCE+//xzLFmypMv9rVu3Dvvssw9OPfVUPPjgg2b5ggULcOihh6Jv375QVRW/+tWv8NRTT+Gbb77BsGHD8M0332C33XbDnDlzsHDhQowcORLffPMN9t9/f7zwwgu91tPOE89RU1MTSkpKzAvawPm9u+WK4n4hpVPOGANjLM5Wr2z0uk1CCJutidrkVt4bbRJCmDe/c3m65ynTbXIe22Tre3XtKYqCMWPG4IvPP7ctu++++/DhRx/hHy+8gGHDhsXZYvzzLiwsRGlpacI2pVPuZZusuB3X7tqY6Ta5PQty6X4C7LYLIdDY2IiSkpKcu5+cJLsOMnXtpWujUe4UXzsiGzZssAkMp9cIgNnDbLtjWJ729va43mdubNq0CbNmzcLUqVNx77332pYdf/zx5mdFUXDXXXfhkUcewaJFizBnzhwEg0EAwKeffoqVK1eib9++2LJlC6ZOnYrf/va3eOCBB1Juq5d40ltt46ZNvugSKaUkWzOEn+ztLVtDoRDGjx9ve5X162eWG0mNTlut77kMXQOZw0/2+s3WHZ3i4mLby00cjRw5EgDw3Xff2cq/++47c1ki6urqMHPmTFRVVWH+/Pldiqm8vDz07dsXm/QQ6IgRI6AoCk466ST07dsXADBw4EAce+yx+OCDD1JspffQMKYEQRAEsRNTXl6OPfbYAwsWLDDLNm/ejA8//NDMDQKAr776Cp9++qn5/YcffsDMmTNRWVmJBQsWxAmvSCQS54365JNPsG3bNuyxxx4AgPz8fEyfPh21tbW29datW4dBgwZ51cS0oa78BNGLXP6rX+Hiiy7qbTMIgsgSCmNZmj4kvX3ceeedOOaYYzB48GBMmjQJ999/P3bbbTecccYZ5jo33XQT6urq8P7776O1tRWHHnooWltb8Ytf/ALvv/++ud6kSZNQXl6OlpYWHHTQQTj77LMxYcIErFmzBnfccQeOOOIIHH300eb6d9xxB2bOnImKigpMmTIF7777LhYtWoS333675weim3gijop8MBIqoMWqydbM4Cd7c8nWgQMHYuDAgQmXGzbmgq1dkUvHtSv8ZCvgL3v9ZiuhccQRR2Dx4sV49NFHsWzZMhxxxBG4/PLLzZwgQBM9w4cPB6AlmA8ePBiDBw/G73//e1tdN9xwA8rLy9GvXz+89dZbePjhh/Hkk09iwIABuP/++3H66afbjv3UqVPx/vvv46GHHsKjjz6KUaNG4fPPP3cdXylb0NxqBJHD0NxqBJFZsj232h1Fo7PWW+3q1jU0t1o38STnaPPmzb7I+hdCkK0Zwk/2+s1W63su47fj6hdbAX/Z6zdbCcINT8TRlvp6X2T9SynJ1gzhJ3v9Zqv1PZfx23H1i62Av+z1m63ZhrPYFCKZfHGKGPYI6q1GEARBEARhgcQRQRAEQRCEBU96q5WWlvoi658xRrZmCD/Z6zdbre+5jN+Oq19sBfxlr99szTa52pWfsOOJOBpaUeFFNRmHc062Zgg/2es3W63vuYzfjqtfbAX8Za/fbCUINzy5Mr7fuNEXWf9CCLI1Q/jJXr/Zan3PZfx2XP1iK+Ave/1mK0G44Yk4amxs9E3PBLI1M/jJXr/Zan3PZfx2XP1iK+Ave/1mK0G4QdOHEARBEESWMLraZ3w/md/FDg0FXAmCIAiCICx4Io4GDhjgm54JZGtm8JO9frPV+p7L+O24+sVWwF/2+s1WgnDDk7BaeXm5F9VkHM452Zoh/GSv32y1vucyfjuufrEV8Je9frM121BYzR94cmXU1tb6IutfCEG2Zgg/2es3W63vuYzfjqtfbAX8Za/fbCUINzwRR61tbb7I+pdSkq0Zwk/2+s1W63su47fj6hdbAX/Z6zdbCcKN3PfVEwRBEARBZBHqyk8QBEEQWYKmD/EHnniOKoYM8UXWP2OMbM0QfrLXb7Za33MZvx1Xv9gK+Mtev9lKEG544jkqKyvzopqMwzknWzOEn+z1m63W91zGb8fVL7YC/rLXb7YShBueXBmrV6/2Rda/EIJszRB+stdvtlrfcxm/HVe/2Ar4y16/2ZptFMS682f0lfWW7Vh4Io46w2FfZP1LKcnWDOEne/1mq/U9l/HbcfWLrYC/7PWbrQThBvkUCYIgCIIgLJA4IgiCIAiCsOBJQnbliBG+SGzjnJOtGcJP9vrNVut7LuO34+oXWwF/2es3W7O+zyx15efUE69HeCKOioqKvKgm4zDGyNYM4Sd7/War9T2X8dtx9YutgL/s9ZutBOGGJ7J5+YoVUFXVi6oyiqqqZGuG8JO9frPV+p7L+O24+sVWwF/2+s1WgnDDE3Hkhy6bBmRr5vCTvX6y1U/46bj6yVbAX/b6yVaCcCP3g8IEQRAEQRBZhMQRQRAEQRCEBU/E0eiqKt/0TCBbM4Of7PWbrdb3XMZvx9UvtgL+stdvthKEG570VgsGg15UkxXI1szhJ3v9ZKuf8NNx9ZOtgL/s9ZOt2caY3iMb+yG6jyeyecXKlb5IwBNCkK0Zwk/29ratq1evxh133IGf//znuOOOO1BbW5twXb/NrUbXQGbwk71+s5Ug3CCfIkFkkWefew5nn302otEoJk+ejG+XL8cee+6JDz78sLdNIwiCIHQ8CasRBJEahxx8ME479VRz8Lk5c+Zg+owZ+Mtf/oIDDzigl60jCCLTKFkaITsb+9iRIc8RQWSRiooK26i8nZ2d2Lp1K4YNHdqLVhEEQRBWmJRS9rSSluZmMMZsUx1wziGEgLX6dMs552CMxY1iavQwcMaLE5UrigIpJVRVhRACnHPz1VMbM9UmKSWEEAgEAmCMJWyTtTzTtidrEwBEIhGzfcnOR1fnKdNtMl7JrgOvrz1ruZQSF1x4ITo7OvDZ55/jqKOOws2/+x369OkTZ0tTUxOGDhuGVdXVKCoqMsvz8vKQn5/fq/eT8zwxxhCNRjPyLPC6TdZnAWMs5+4nZ5uM5Zxz27rJ2tpbbXK7DjJ97fXkWVDUty+yQXNzM0pKSvD0gPHow5WM769dqDi7fiWamppQXFyc8f3taHgSVvth82Y0NTYC+o1QWlqKoRUV2FRXh8bGRnO9gQMGoLy8HBs2bEBrW5tZXjFkCMrKylBTU4POcNgsrxwxAkVFRahetcp2M4yuqkIwGMSKlSttdkwYPx6RSARramrMMs45Jk6YgLa2NtTW1kJVVSiKgry8PIwZMwZNTU3YuGmTuX5RYSEqKytRX1+PLfX1ZnnW26SLuV122QXRaDRxm9avN8vzQqFea1NhYSGqq6u1h6F+HXT7PGW6Ta2t5nVQUVGRnWvP0qZQMIhZhx+OLVu2oKW1Ff/4xz+w3377Yb99941rU2tLCwBg7Lhxtv1dcMEF+O211/bu/eQ4T6NHj8a2bdtQX19vXgM5cz8527RmjXkNcEXJufsprk1SYtiwYSgsLMTK6uoenadMt6m0tNQ8vsZ1kOlrr9ttamjAlKlTQRBOPPEcffrppxg3diwURVPDvf2vMNG/jUgkgupVqzBu7FgEAoGc+VfoZruqqqhetQoTxo+Hoig5868wUZuEEFi+YoXtOujtf4WJyqPRaJfXQTb/6c4+80xs/P57LF68OM6WhoYGDB8xAitXrEBxcXFOe46klHHXQK7cT85y67NAUZScu5+cbbI+D5yTpfb2/eQsd7sOctVzFI1GUVxSgmxgeI7+OjB7nqPZW8hz1F088RwZbmnjRjAwLnAn6ZY76+1OuWGj8W7syysbM9Emwy1t2OwkUXlvtSnRddCd85QpGznnaV0HXl57iWzcfbfd8PFHH7naYmzXt29flJaWJmxTOuWZapOqqhl/FnjZJqetuXY/OW1J9ixwW9/YJtttSnYdZON+Sqc80X4JghKyCSKLvPLKKwhbQijNzc2Yv2AB9t1vv160iiAIgrDiiecokTLPRcjWzOEne3vL1rXr1mGvyZMxdswYcM7x8SefYPfdd8d9997bK/Z4DV0DmcNP9vrJ1mxDXfn9gSc5Rx3bt3thC0HsFDQ0NGDp0qUIh8MYM2YMxjmSra00Nzdj0ODB+KGujvIGCCID5BcUZGU/Rs7Rs+UTspZzdPrmFZRz1E088Ry1traisLAwLlEw15BSoq2tjWzNAH6yt7dtLSsrw2GHHZbSusZ/Fw/+w2Sc3j6u6eAnWwF/2es3WwnCDU98n7Xr18f1KshFhBBka4bwk71+s9X6nsv47bj6xVbAX/b6zVaCcIOmDyEIgiCILMEZA8+CRy0b+9iRoaw5giAIgiAIC56Io7xQKOdjy4A2PgbZmhn8ZK/fbLW+5zJ+O65+sRXwl71+s5WI8e9//xsnnXQSpk+fjssvv1wb7T4JdXV1uPHGG3HUUUfhhBNOwAMPPIDOzs6017Hypz/9Cfvttx8ef/xxT9rUXTwRR2P0bsm5DuecbM0QfrLXb7Za33MZvx1Xv9gK+Mtev9mabZjCsvZKh1deeQVHH300Jk+ejCuuuAKffvoppk+fnlDINDU14YADDgDnHPPmzcMpp5yCBx54ACeccIJtbsiu1rGydOlS3HHHHVi9ejW+++679A+uh3iSc9TQ0ICSkpKcvxmEEGhqaiJbM4Cf7PWbrdb3XMZvx9UvtgL+stdvthIa11xzDebMmYNrrrkGAHDAAQdgyJAh+Otf/4o5c+bErV9YWIhvv/0W+fn5ZtnQoUNxyCGHYPny5dhll11SWsegpaUFp59+Oh599FFceOGFGWxpanhy5W7ctMkXXSKllGRrhvCTvX6z1fqey/jtuPrFVsBf9vrNVkILfX3zzTc49thjzbJ+/fph2rRpeOutt1y3CQQCNtEDAEVFRQBgzgKQyjoGc+fOxY9+9CPMmjWrZ43xCOqtRhAEQRA7KM3NzbbveXl5yMvLs5XV1tYCACoqKmzlFRUVWLNmTcr7uu222zB69Gjstttuaa3z1FNPYdmyZViyZEnK+8o0JI4IgiAIIktwhYHz7HXlHz58uK38hhtuwI033mgri0QiABAnmgoKCsxlXfG73/0OCxcuxOLFixEIuEsLt3VWrlyJK664AosXL47zMvUmnoijIh+MhApoPRPI1szgJ3v9Zqv1PZfx23H1i62Av+z1m607Ohs2bLBNH+IUQIAWQgOAbdu22cq3bt2K/v37d7mPu+++G3fccQdeeeUV7Lvvvmmt8+KLLyIajeKCCy4wyzZt2oTHH38c7733Ht55550u958JPBFHlZWVXlSTcTjnZGuG8JO9frPV+p7L+O24+sVWwF/2+s3WHZ3i4uIu51YbO3Ys+vbtiyVLlmDatGkAtHysJUuW4Kc//WnSbe+9915cf/31eOWVVxJOi5RsnXPOOQeHHnqoreyEE07AkUceiYsuuqir5mUMT66MzZs3+yLrXwhBtmYIP9nrN1ut77mM346rX2wF/GWv32zNOgoHy8ILSuo/78FgEGeeeSYeeughc2yjJ598Ehs3bsTZZ59trnfNNdfYBMvvf/97XHfddXjllVdw+OGHu9bd1TpDhw7FfvvtZ3vl5eVh2LBh2HvvvVNug9d4Io621Nf7IutfSkm2Zgg/2es3W63vuYzfjqtfbAX8Za/fbCU07rrrLowfPx6VlZUYM2YMLr30UvzlL3/BhAkTzHWqq6vxzTffAADWr1+Pyy67DIWFhbjuuuts4mbx4sUpr5OrUEI2QRAEQezkFBYW4rXXXsP69euxdetWjB8/Hn369LGtc/vtt5sJ2oMGDcJHH33kWte4ceNSXseN+fPnY+DAgd1phmeQOCIIgiAIAgAwYsQIjBgxwnXZ2LFjzc95eXnYb7/9ktaVyjpu7LXXXmlv4zWeiKPS0lJfZP0zxsjWDOEne/1mq/U9l/HbcfWLrYC/7PWbrVnfJ09/ao9u7Qe5f/xzGU/E0VDHwFG5CuecbM0QfrLXb7Za33MZvx1Xv9gK+Mtev9lKEG54cmV8v3Gjb3omkK2ZwU/2+s1W63su47fj6hdbAX/Z6zdbCcINT8RRY2OjL7L+pZRka4bwk71+s9X6nsv47bj6xVbAX/b6zVaCcIN8igRBEARBEBZIHBEEQRAEQVjwRBwNHDDANz0TyNbM4Cd7/War9T2X8dtx9YutgL/s9ZutBOGGJ73VysvLvagm43DOydYM4Sd7/War9T2X8dtx9YutgL/s9ZutWd+nwsCz0JWfU1f+HuHJlVFbW+uLrH8hBNmaIfxkr99stb7nMn47rn6xFfCXvX6zlSDc8EQctba1+SLrX0pJtmYIP9nrN1ut77mM346rX2wF/GWv32wlCDdo+hCC6A1kiv9YjfWkSG0blvvhN4IgiFyHxBFBZIpUBVC29knCiSB6HcY5WBZynRh5xXqEJ+KoYsgQX2T9M8bI1gzhJ3szYmuGhJCnvdXcbPRQMO3010AG8ZO9frOVINzwRByVlZV5UU3G4ZyTrRnCT/Z6YmuWvEIZ763mbEcPxNJOdw1kET/Z6zdbCcINT66M1atX+yLrXwhBtmYIP9nbbVuNvJ8shsuy3lutB23cKa6BXsJP9vrN1mxjdOXPxovoPp54jjrDYV9k/UspydYM4Sd707K1N/KGrLvvzd5q1ran4FHaYa+BHMBP9vrNVoJwgxKyCcJJhgVRfX09PvjwQzQ2NGLX3XbF1ClTMro/T0hTKBEEQfgZesoRhEEWQmb33nc/DjzoYPz9b3/Hhx99iOOPPwEnnXwyouFOMClcXwASLku0fkbJcmiRIAgi23jiOaocMcIXiW2cc7I1Q/jJ3jhbM9XTzKXeSbvtgmVLl6CgoAAAsH7DBuw5ZW889X/P4II557naan3v7n4BQHrt8TH2w2I2+vYayHH8ZK/fbM02TGFgWcgHYjR9SI/wRBwVFRV5UU3GYYyRrRnCT/aatkoBeJhzkIrXZtbhh9u+jxg+HFWjRmHVqlXudXrYld9pn2diyfBugZ4FmcJP9vrNVoJwwxNx9O3y5RgzejQURQGgXXCccwghbAlv6ZZzzsEYg6qqtv0Zat/Z0yBRuaIokFIiEolg9Zo1GDN6NAKBgCc2ZqpNqqpi9Zo1GDd2LBRFSdgma3mmbU/WJiEEVlZX266D7p6njLZJjSIajWL1mhqMGV2V8DpI5TxZxQbnHLIbbapetQrLV6zAry6bByFEnC3hcAQA0NjYaCvPy8tDfn5+D6891dYm1aET0z1PUkqsrF6BMaOroASCqZ2PXnpGWJ8FiqLk3P3kbJP1eeD8Qe/V+8mlXLsO4p8FXj7LvWpTNBpFvu7FJQgrnoij9vZ2VFdXm6N+lpaWYmhFBTbV1aGxsdFcb+CAASgvL8eGDRvQ2tZmllcMGYKysjLU1NSgMxw2yytHjEBRURGqV62y3Qyjq6oQDAaxYuVKmx0Txo9HJBLBmpoas4xzjokTJqCtrQ3r1q1DY1MTqlUV+fn5GDNmDJqamrBx0yZz/aLCQlRWVqK+vh5b6uvN8my3SQqBxqYm8wZO1Kba9evN8rxQqNfaVFBQgIaGBtt10N3zlLE2DRyADd99h5aWVjQ2NqJaCAytqEBZWSlq1q5FZ6e1TcP182TvkjymaiSCgQBWVNs9PRPHjUUkGsXqmrVmmcI5Jo4fh9a2NtRu+M7WprGjq7Bx0yaccvpPsdtuu2LXXXfD+g3fYeSIYaivr8fm+q0AgJaWVgDAuF12s+3vgvPPx3XXXI3ygQOwfsN3aG1vN5cNHTIYZaWlWLN2nf08DR+GvkVFqF69BqqtTaNc2sQwYfw4RCJu1954/TxtiLUpL4RRI0eio6MD1atWaz/gjOXM/WRgXHurV682nwVKIJBz95OzTVIICF0UrFq92rVNufKMKC4u1u4vy7PA62e5V21q2LYNU/feG9lEC6tlYYRsUF5gT2DSg76Mn376qenhAHr/X2Eyz1H1qlUYN3asLzxH1atWYcL48b7xHC1fscJ2HfT2v0KzXIq4f4vVq1Zj3NgxKXmOnB6itNsk1Lg2dXR04PiTTsHWrdvw+r9eRv9+/Vxtb2howrBRVaj+5ksUFxd3z3NkyQnqzv3k9Cgl8xwtX7ES48aOsT8LlECv30/OcuuzwC+eI+N54AfPkduzIFc9R8UlJcgGzc3NKCkpwb/2nIpCJfMdxdvUKI754lM0NTWhuLg44/vb0fDkDDHGzAeMlUTJbumWO+vtTrlho/Fu7MsrGzPRJsaY+UrWpkzZmG55ouugO+fJExtNUaPYylO9DpgUCHBm2z6Z7QCgcEcOgy7MrOtv374dJ55yGrZu3YY3/vUKBg4ckLBNip642bdvX5SWliZua0rlEpBSs9El3yhRmwKWJhl5Sm7nSVVV92tACnAGgGfuWu3OM8Jpa67dT05bkj0L3NY3tsl2mxJeBwlsTLfcyzYl2i9BeCKORldVJbwAcwnOOdmaIXLK3i4So5PZ2q2u8GlsYwijLVvq7cIogQOX614Czpj7Ot1NKO3muEXG8XFL5u7yGnD0butNcup6TQE/2es3WwnCDU/EUTAY9KKarEC2Zo6csDdFoRIM2i/9tERRtwSUJmwuvPhneO+/7+Pyy+bhuedfMBePGzsGR8w6PNHWXdabkFTEUzfmV0skkpzHNeH+ckAg5cT1mgZ+stdPtmabbE3twXeirvxSSixbtgwrVqxAS0sLBgwYgMmTJ6OysrLbdXryhFqxcqVv5tEhWzNDr9ubxsCEmq3VZo+zlIVRqvuQMv6ls9dee2LuhRegva0dtevXm68tegJ2vK3S9p42SWxJvE3qx9J6/KzH1ct9ZIJev17TxE/2+s1Wwr/88MMPuOaaazB48GDstddeOPPMM3HFFVfgJz/5CUaOHIlJkybhkUceQWdnZ9p10/QhhP/p1o+s1H/Uu8g5SFk4pSZefjXvktTqyyRWW5N5ltIIvXV7dO4c8SIRBOEvnn32WfziF7/AAQccgPvvvx/Tpk3D8OHDzcT/b7/9FosXL8aTTz6J++67Dy+99BImTZqUcv0kjgj/0o0f45R/xLtaZ0eZsNLZjkRiKeV8oRRFZ7fqJgj/wxgDc3bcyMR+xI4fVvv4448xduzYuHJFUbD77rtj9913xyWXXIJ33nkHLS0tadVN4ojwJ2kKo7RCZ0mXeyiKUg3RGe9dre+FuDD215VI6mJ/yRK3E++bvEgEQaTG6aefnvK6M2fOTLt+T8Y5amttNcexyGWM8THIVu/Jqr09FEZxtmZaEPUgt6apqRmDRozCD+vXoqSkm2OV9FRwdHU+9foTXQNpT1OSBYFE91fm8JutBX36ZGVfxjhHr0/dB4WBLIxzFI3iqE//t1ONcxQOh7FmzRps2bIFI0aMwMiRI7tdlydPoUgk4kU1WYFszRxZsTcNoZEshBaJRruuL9UE5rjthP2VxLZUXums3117kreni+NgqdM8ri5tTX1/2UnWpvsrc/jJVmLH4Omnn8bIkSOxyy674JBDDsGoUaMwdepULFmypFv1eSKO1tTU+CLrXwhBtmaIjNub5g9msh9jIQRWr6mBUON/yLV9pSmKuhAfKYsYl3qFUHWb1S5WTmNf3RVLyY6LFBCqNn1Komsg7YTtDAokur8yh99szTZc4Vl77Sy89dZbOP/883HJJZdgzZo1aGhowBdffIFdd90VRxxxBLZt25Z2nZRzROQ+Hokis66EHpY0BVF3bOjJD34621pCU3FhRWfYKt0BIZPlJZm5Ue4J2WnnIlEeEkEQXbBgwQLMmzcPV199tVlWWlqKp59+GlOnTsU777yDk046Ka06SRwRuY1Xwqir8FkP7EkazupGfXZE7D3ZuskEj2OdpGIpnZ5jSUVS8nqYFCSQCILwhNLS0oTTKw0ePBhlZWVp1+nJE8dPQ7CTrZnDc3szKIwUzgGJ9AZFtNSTMGyVKFzlDGWlu05Ptu3CNte2pBN2s4TbFOc10F0PW9w+vA9/7PT3Vwbxk62E/znmmGPw6KOPYu3atbbyRYsW4dtvv8Xee++ddp2e9Fbr2L69p1UQhJ0Ufwy75S1K9ZJPxUuUrtcozR/55uYWDBw1AVvWrkBxcd/UN0zkaUmx3NWrk6r3JlEPpSTbp+xFIg8S4TH5BQVZ2Y/RW23RvvtlrbfaEZ98vFP0VnvggQdw8803o7GxEZMnT0a/fv2wfv16fPvtt5gwYQLGjx9vrnvJJZek1LXfkzPU2tqKwsJCX3TbbGtrI1szgKf2ZlgYSSnR2taOosI+7ra6eFa6rD+VdQzSSAKVeiK2FGrq23GeOKzmLDfEhiMMZm2zTLBOnK3W4+rmOUgSHks5zOZRiG2nvr8yjN9sJfxPv379cOqpp9rKRo8ejRkzZsStW1hYmFKdnoij2vXrMWH8eChKGqPi9gJCCLI1Q3hmb6aEkeUhKIRE7XffY+LYMVCsE0B2JYq6I4h62HPLKo5S2UYy7r5PN8HkFEtu3y22diWSbMeVJchHyhGBtNPeX1nAb7YS/mf27NmYPXu2p3VSQjaRO/RUGHU3jNYTUZSCGPIkYTuV/B/GXfflKpicYskqjLrwJqXqSdLWke4CKcF22fYgEUS2YQoDU7IwfYjMba9drkPiiMgNMiGMUk22TlR3MhFk/S66EFeJ7POaBKE0195pVpu5Qxh1IZpcRVJXAglI2YtEAokgiN7GE3GUFwrlfGwZ0Cb8I1szQ4/szbIwYgzICwXBIGB02IzrqdXVZ8AmMFJO1E7Rxrh1UhmYMoX8KadYsgmlrrxJLiLJKpAYhH4NJGlLGgLJtC8Z3RRIO9X9lWX8ZitBuEG91YjeJQUR0ZP8oq62SVsUJRJEXbXDaVOKgrC5pQUDxu2F+urPUdw3hd5qTqGQ4rxogEOIWBOqWdefZaJ1XPfpYlNPe7KRB4noJtnurfbmQQdkrbfa4f/9cKforZYJPHmiNDQ0+CKxTQhBtmaIbtnrtTBKZQ4wKSCERENDI6Sq2pdZ1on7LIQpjGxjAiXKBTJskRIQamw9/ZV0jjQRNV9Sn+JEqrGypHOrOV9CtduS4JjEtcvS3oTHxCEypaqiobEJQlWTn1s3W5Ksn1Lyepphy53i/uol/GYrseOyatUqrFq1qlvbeiKONm7a5IsukVJKsjVDpG1vJoRRqvsTKjb+sFmz1e3HvitRZH05bTBfSYSQiMaLGCkAEdVeljJbV/4k65n7chFP9nUSCCUXe53t7+pYSSmxse6H2DXgoTfNa4G0w99fvYjfbCXsfP3113j33XexdevWlLdZuXIl3njjDbS0tLgu7+jowBdffIH//ve/aG1tdV2nra0Nn3zyCZYtW4bOzs5u2e7k1ltvxYQJE3Deeedh8+bNaW1Lvmgi+6T5L7/L7bsVRpMwp+Zw+9FPJoqc+3YIIptAcYoYN1GTROzEiZBUtnOUJbYnuVBKKpJcj1vseDnrSnxuuhduTFwfeQIIojs0NjZi2rRpmD59Oq644goMHz4cDz30UNJt3n77bcyYMQMzZszAUUcdhTVr1sSt88Ybb6CqqgpnnHEGrrjiCgwbNgz/+Mc/zOWRSASXXXYZRo0ahXnz5uHUU0/FqFGjsHDhwh636cYbb8Tbb7+NiooKfPnll2ltS73ViJwk5eTrrsJorvWJ+HWsIsC5jZstDu9IdxK6E7bRaoMeVmNq1PyMBFN0xM2Rlmg8Ics6sW30dxY/7pNRYk/eNirjjn1JW9tS6tHmTNROsG5a87ERRI7CFQ6uZP465jK9fVx++eVoaGhATU0NiouL8fzzz+OMM87AQQcdhEmTJrlus2HDBlx33XUoLy/H7rvvHre8qakJp512Gn7+85/j1ltvBQC8+uqrOOWUU7DvvvtixIgR2L59OyorK1FbW4sCPf/r2muvxamnnooNGzYknDMtFUaOHImRI0di+vTpaW/ryRkq8sFIqIDWM4FszQwp25vCP/uMCiP9c1GfgoTCKDVPkcO7ksiz4+a9MYSO4Y0RAlDV2MvmjTL2a9m3dV1LHUa9rl6iRGG4OPvT8CRZj52+TlGfPrCKz5ST1lP0IHkVXtth768cwG+2EkA4HMZzzz2HuXPnmsnbp556KiorK/HMM88k3O6cc85JOhXHsmXL0NTUhHPPPdcsO/bYY1FYWIi//e1vAIDi4mJceumlpjACgLPOOgutra349ttvU7L/iSeewHfffee67JlnnsH8+fNTqseKJ+KosrLSFxMNcs7J1gyRkr29KYwsQkdhwMihg6EwvdwQF9Yf/+6KIl2EOMWQTQTZxE/y/B9jpGmFOfKj4uyyvCyiyVUsuQillEUSLOLRaJNhK+cYOXSQPqmvsK2f8Dw625LgPFrxQiDtkPdXjuA3W3d0mpubbS+3fJ7q6mq0t7djr732spXvtddeWLZsWbf3XV5eDgBYt26dWdbQ0ICmpiZ8/vnnCbf78MMPwTnHmDFjUtpPdXU1Jk2ahBdffNEsa2xsxGmnnYaLLroIAwcOTNt2T66MzZs3+yLrXwhBtmaILu3tbWFkWS6kxA/12yCktHmLzHVt67uIIqfIcBFECcWQdR9Wr5Jw743mnD7E2ZvNNbnbZrdDLKXYhoQiyU306MdQCBU/bG2AEJbeajkqkHa4+yuH8JutWUcfITvTL+ijcA8fPhwlJSXm6/bbb48zqbGxEYA2R5mV/v37o6GhodtNnTBhAo499ljMmTMHjz32GJ577jkcc8wxKC0tTVhvTU0NrrzySvzyl780xVVX3HHHHfjtb3+L2bNn49xzz8XChQsxadIkrFy5EkuXLsW0adPStt2TnKMt9fXo37+/F1VlFCkl2Zohemqvl8LI9YfY8i6FwJatDRhQUhRLdUm0H2udLnXZ9meGmhL/wCcVCS7HwD7xbNS+0DlJrCW/J27cIcMmVTXze8zV4/aq18m4ZZkjJ8lou8V087iW9gWUAMzcIf3dlodkLHPDyxykBNvubPdXNvGbrTs6GzZssI1zlJeXF7dOKBQCAGx3jFnY3t5uLusuL730Eh5//HG8++67iEajuPrqq/HQQw+52rFx40bMmjUL+++/P+6+++6U98EYw69+9SscdNBBOPjgg/HUU09h9uzZeOKJJ7ptPyVkE5mni3/52RRGAOzeIud0GYkSrV3EkekhcrPNbXu3dgnLWEvm4thyGY2Y78bn2Iz3lm25EqvXOgq23j5TRLgIJQYBcO4ukgw7YjvSF1hEknV/1uNnFUEWkWKKmmwJJILYiSkuLu5yEMiRI0cC0ITU5MmTzfLvvvvOXNZdgsEg5s6di7lz5wLQvHVz5szBRRddZFtv48aNmDFjBsaPH48XX3wRwWAwrf2sWrUKP/vZzzBgwADstttuePnll3H44YfjrLPO6pbd9FQhMksq4Y9UtvNYGJk/9wmEkS0Hx9k1XlryiFzCZWZozBm6UiPaS6im2JFCxD4bAkio2isa1l6A9q6XO9e31gGhxvbjFvKztsVosx5eNPKTXHOorMfDeT4SetASvCOBaIw7rx518+/udgSxk1BeXo699toLCxYsMMvq6urwwQcf4MgjjzTLvvjiC3zyySdp1d3c3Gz7/uyzz6KhoQFnnnmmWbZp0ybMmDEDY8aMwT//+U9Xr1IyXnrpJey1114YOXIkvvzyS7z++uu45557MHfuXJx66qndCg164jkqLS31RdY/Y4xszRCu9qbwo+TqNcqwMOJSoqxvHzCrd8LIKzLqcvEYJfQUGcLBuU8zJObiKXLxGLlhmMdYkm0s5ZIr2geuxDxkhqeJKzEvj9WjZPUmCdGlJ8nmRbJ4kJhxXMG0fXMXz1EGPEjdCa/tEPdXjuI3W7MNZwycZ36/PM223XnnnfjRj36EgQMHYtKkSfj973+PPfbYA6eddpq5zi233IK6ujq8//77AIDa2losX74ctbW1ALRE6rq6OkycOBGVlZUAgBtuuAGKouDAAw/El19+ibvuugv33Xcfxo0bBwBobW3FoYceiu3bt+PCCy/E4sWLzf3ttddeGDRoUJe2L168GH/4wx8wZ84cs+zCCy/EIYccgp/+9Kd4+eWXcc4556R1PGhuNSJzdCec5lqW4BJNUxi5h7js3iJzueVzyqLI3JcaE0QJxJBt6hLdPjeaW9vQ/+CTsPW9F1FcVBi/gqO3DVMUx3LF9s44j5VZQm2mSDIrYmb9tpCcZT3bNtYHsXU557ayuHdjPUeZvVGpzcXWpUCi8BvhQrbnVlt82MEoCmY+o6U1EsWMt95La261jz76CI899hi2bt2KKVOm4LLLLkNfy5yOt956KxoaGnDPPfcAABYsWIA//elPcfVcfPHFOP744wEA0WgUjzzyCN59910MHDgQZ511Fg444ABz3U2bNtm6+lv57W9/m1IydTgcTphbFIlEUFdXh+HDh3dZjxVPxNGaNWswZPDgnO8WKYTApro6sjUDxNmb6TyjHggjISQ2bm1ARb9ScGYZtNAhdGxhIjdRlMhL5CKITDHk5kUCzMRrG0KgsbUd5Yf9FJvf+htKi4viVmHcIoZsn3XvjOKynCtx3iS9MneRxB1iyLm+/llIaMe1fxm4vl9zOefeCqQE66UqkHx/f+UwfrO1T6HLn44M4Adx5CeWLFmCPfbYI6WE682bN6OxsdH0VqWCJ1duY2OjL7L+pZRka4bwxF6vhZGl+7p1mYREQ3MbpFRj9TheprfI6Iqvbx/XfV615/3YcoNU/RWJAFHtJaNhy0vbVoQ74vOIwh2Q0TCEnnMkomG9zL6ebVt9GxkNx/YXiZh2WHOZbDYb+UnO9hnnQB8KIOFx0o+NlEI7rpDx50gI93Ok02UOksfTjOyU91eW8Jut2YYpPGuvHZlFixZh/PjxuOeee7Bx48a45VJKfPbZZ7j00kuxyy67YMOGDWnVT73VCO/xIpzWhTByLXMKIyT40ZUSgNSTjOH+Y2/1FrmFz4zQmcNLZPMQ2brhi9hny/rmutbmWEJuMhIx37XPkbjQmeSOXmsAwPU6uWp6l6SRBwS9F5pQAa5oNnFhC7kxva22nCQhNMeLI8cnNh0J7Oh5PmZOkBDa37EEOUjO7eLwIv8oWX4TQRC+4be//S0OOOAA3HTTTbjyyitRWVmJUaNGobCwEA0NDfj222/R3t6OU045BZ988glGjx6dVv0kjghvkQKAknBxaoP3dS2MXBOgjfdEwsgmdoyBHRHvLUoUQrOKIiDmiYEuaCzlcYJI2MNqcTlHRn1xZRaxZhVbQEwIWepiil4/t6zjFEpcMYWSNVgVJ5IYjyVgGwLJ6P7P47WQFqG0DD7JWFoCySZsUhVILqQkkAiC8D0zZ87EzJkzUV1djbfeegsrV65ES0sLJk6ciJ///Oc4/PDDuzU6NuCROBo4YIBveiaQrZmhR/am+WOVVBglXCcmjDgkyksLwYzwj5swcooiwO4tcooiQxABgBBxgsgmhoSK9o5OfLG6FsMGlGJEeX9I4XIMhApEOrTPkQ7IqPN2jdhzh2AIHMUUTEwR8UJJ/84SiSTo3iDdS8R075GbF8kqkBgYBpUUacfVOOZuAsk4L10JpFTopidop7q/sozfbCX8z7hx49LKJ0oFT8RRqkN89zacc7I1Q3DOUT5wQNJ1vAindSmM3HqlOccvgsSgkkJd+MiuhVEqosjpJXIRRBAqfmhowl1/fw0vvbcEja3tmHfiYbjxzGMdTbWIPDVivsuwJpSYJclVArowilh6pMXEkATihRJXLMJIjRdJQtWGBDC9SLotxv4SCCTOOAaVFgKQkKbocRFIAkm7+XfZxd+D8Bpn/nluAf56HvjN1qzvU2HgSha68osdX/gtXLgQBQUF2H///ZGfn+9p3Z5cGbW1tb6ZR4dszQxCCNSuX98ze7MgjCAFVDWKtXXbIFQ1bWFkTbC2JlVLoZqJ0EYStHUgR2O9tRs2onJgKZY+dC1GDOyn1WdNqA53xAZ/jIYh9FGxhZHsbSRmxyViR8xtrcvMulxtt9jvZru17VYPm/XYWgaPVFUVa+u2QrUOJuk4B+Z57GKgyLQTtNPEl/eXT+z1m62Ef/nXv/6FmTNnoqysDDNnzsTNN9+MDz74ABE9V7MneOI5am1r803PBLI1M0ihorU1sb0pj2mU7jppCiPj1drRCYg+gGTu66ToLXL1FDmFhSVPaZ8xw7BP1RDDeEAKyEg41h7Hw1pEoua7tN7wnFs8QkrMRsCSZxTR1jO9QKrNm6RtJyADMa+QdboQdy+SYg+zGf+vhAAD0Lq9MyakDHtS9SAlO8fdmEMtmfdISonW1lb/3F8+eh74zVbCvzz88MO47LLLsHjxYixevBgPP/wwrr/+ehQWFmLatGmYOXMmZsyYgcmTJ0NxjgHXBZ6IIyklVGtSKGPgnEMIYbv40i3nnIMxZqvbKAfiVX+ickVRTBuNd69szFSbDFuNV6I2Wct7s01A/HVglqv2CVONcZBsbZKAonC9TZZ9QoBzDqmqEFICiAkghXMIKU1RwvREa84ZhNBDO5ZQGodmn1CjkEJAVSWYAnBICFW1CSNjugw1GtXqN8qFCggJ1SGKuP5ddfRg41LotlvaqgpwoZ1foaraPoQKBt0WwDwGkXAnAKCpqQkyHDJDZ3nBAPKDChSuaNubvdQ4OAAuVAgAksWEEecKGItAZfo4R6qWnK1IQHIVgitgXAA8CsYVcFXRBoHkEuBSD8dJKIGAZjskJJO6KJEAA6TumdNOiCaiuBKAALNcMwKMKWAKIKIqJGfaeWVc2y8EVD1R3hA3jDP9vAqb04gr1vtJNQWSeT+pEZtAMsqtzwIg9+4n5zPC+jxI9XnYW20C3J8FXj7LvWqT0x7Cf4wdOxZjx47FhRdeCABYsWKFKZbuueceXHXVVXjqqadw9tlnp1WvJ+Koo6MD1dXVZi5EaWkphlZUYFNdHRobG831Bg4YgPLycmzYsAGtbW1mecWQISgrK0NNTQ06w7F/0ZUjRqCoqAjVq1bZbobRVVUIBoNYsXKlzY4J48cjEolgTU2NWcY5x8QJE9DW1oZ169ahsakJ1dXVyM/Px5gxY9DU1ISNmzaZ6xcVFqKyshL19fXYUl9vlme7TVIINDY1QQiBaDSasE2169eb5XmhUO+0afgwFBQUoKmpCdWrVpsPSK1NAayoXmU7TxPHjUUkEsbqmnVmmcI5Jo4bg9a2dtR+971eKpEXCmHcyOFoaG7Bxh9+MIpRVFiAkRXl2LK1AVu2NWmFUqKsuBDDBvbDxvoGNLS0ar3SAJSX9MGgkj5Yv6URLe2daGjrxPJNDRhe1gf9+wSxenMzOqL6mEZSYlQxR9+QguX1HZookxJSCIzpoyIIFctbFUipe04Ew4RAByJCYk20j1kHlwITsBVtCKJWlprlIRnG6OhmCAlsZX2wgg0EFKBPdDuGd25GfbAEW4MlAICWgDb6/K7z7rUdw/N/ciyuOXE6BnQ2Y0N+OdpYvt79HhgSbkYZC6MmMABhBLX5aVVgBGtFkSJQLQshjKk/GMOYAhVBpmJFpwIwAYABTGLXfkBEBVY1R7QkHQCcK9h9SF+0hiVqtm3X3UsMecEAxpSXoDOiYsV39Zp3CQxFBXkYNWQAtjS2YnNjq2l/WXEhhpUPwKb6BjQ0t+o5RAwD+5di0ID+2PD9JrS2a22XjGHooHKUlZVhzbr19mtv2FD07VuE6tU1mjDVr70xVaMQDASwvHoVLIMNYML4cYhEoli9Zg0aGxtRXV0NJRDIrfvJ5RkhhYDQRcGq1att10JXz71st6m4uBjNzc223wSvn+Vetalh2zZM3XtvZBOmMLAs5ByxnSDnyA3GmO3Vp08flJWVpV+PFyNkb/z+e/Tt29dU+7nqOYpGo2hubkZxcTEURcmZf4Vutgsh0NzcjNLSUrMetzblxD9dpv1TbGhoRHFx7DrgXAufxJ0n/Z41y6XRJovnyMg9YYDCoHuCVFtuisK55vERsXIGBs6ge4IsuTKQUCChRlUIIdDU1omSPkEEWMyjZEzqCqFqNgoBNRLWQ2cSUqjgUS0nRwCxkFk0onmChICw2CJVFYoeglOFiCVaqwJMVTH1modx7JQJuPaEGYCqLePaEIqQ+g968/ZOjLr0Xnx1x89RZEk4zAsoyA8q4AqHQGwUa6ZwLeET0MNhxotDUbSEa5UpsVGyuQIlEAS4AmEkdCsKEAhC4QrAmVaPEjTHV1ICAUjGIZWg6R2SjINxjobWDhQX5oMrsd5tiu45EmD6+kw7T5xBSAZhGYWbcQWcMc1zhNjI3IwZ69vTjThnYJzb7yfG4+4n6fAoac+CFu16VQK5dT+5PCOEEGhpaUFJSQmc5KLnqKGhAcXFxfZnQY56jvpmafRoY4Ts/x47M2sjZB/06js77AjZBqtXrzY9Re+++y5aWlpw4IEH4pBDDsEhhxyCvffeG8FgMO16PTlD/fr1cy1P1BMg3fJEscJ0yhljCAaD6N+/f0Zs9LpNiqLYbE3UJrfyrLbJFDEM/fvHXwcMLjbq2yiKEpdYq7WJmYLJyCPiRvhGD7dAHzNHgdTzVoy6NWGlMKMCyzaqCoVpImxA3zw9x0hbn4uoHg4TmiCIRCxhsWgshCZUMGmIHj3/SI2YITcF9twkI6GaqQJQNYEkVaGZKyWYKsDCEU3MQXPyWHuryU4trFbIgCJjqhMjLBkWgGIIGv2cRACpcAjOwRQBpmj18kAQEAok59omqgpIRT+W2vFRpD4MgACYCl1camKFiSgACRYMam3l0EbTDgQBJgEmISHRv69lnioWS+nikOCMad91j5V2LelCTvsCI9tJMa4xc542Y3333mu2a8wSRjPKnblH2rPAfr3mxP1kwWqLoigJn7Nu6xv0Vpucz9lkNqZb7mWbcn16EyI5P/vZz/DEE0/gsMMOwyGHHIJ58+ZhypQpCAR6Lm08uTJWr17ti6x/IQTZmiGEEFi9Zo39H10Pk7AT9k7Tdhhfp5sT1NbLSluuqiqq6xq1f7FSmN4iW48uEetFBqHaenFZe4KZvcuMbTu1nmQi3AG1sxMiHIXaEYbaEYaIRCHCUUhVQA1HzH/A0Y5OiEhsPesr0qnl70Q63ZdHOzrNlxqOQKoCIhy11SfCUd0WvZdbZ4etN53Zy83a3hSOg+lp04+xUFWs3NQA1enecZ5zy7no+pym2HvNWb8D57Xodr3mMn56HvjN1mxD04d4x5AhQ6AoCr788kt89dVX+Prrr1FbW+tJ3Z54jjrDYV9k/UspyVYvsfzgSCnR2ZmmvWmtG//jaOsublnP2TPN2XWcSYGOiC6MTK+Qau+NpnfPhx5GA6AJCCFi747tpF4uVf1l+SxUzdMUjqpYunYjICS2h6P4rr4RH6yoRXF+CBMGxsfF1bBqvquOAeuYwvXhjbR3xjmE8VDUv3NF0R6UgoOpxkNTaInlgZA5tpGMwkzcloDWsy0QgoxEtPGRAgCiANOfGLaebVFoHiTJ0Bk15mVT4sZBgr5NXA8yo2dbohG0U8HoDZcicddrOvvqBXzxPNDxm62Ef7nuuutw1VVX4eOPP8bixYvxzDPP4Oc//zkGDhyI6dOnm690pw4BaPoQIkN47jWyfhYivn49PJZQGDmXQ2peD4iuhZHVS2J9d4TPTCGkd7+3iiJjWUNzG25+9b+ABCqKC7Guvgm3vf4hJg7qj1t/dECsOXoOkhrW6lI7w1ClsP0bZKoecrKWKVzrwcU1ISSFAFNjIgkRgAcDumAS4IEgzMEgFQWSK5pQ0d+Nrv8MMAUSuAoWCMUJJPAAIA3RqvW9SyiQAG25IWisAsk4147PXQ4Oabse4tdJe/RtgiBynlAohIMPPhgHH3wwbrjhBnR0dOCjjz7C4sWLcd999+H888/HM888g9mzZ6dVL4kjonukInSSbp8gBOb2PZVwWlfCCHAsl2aOUVfCyCmKTGGkrysiUVdPkbVc6OVloSDmn/tjM6/IWB8Aoh2xHktmmS6Ooh1hRIVdHJkdICwudKZyUyxZhZJQOHgwAK4oEIianiSpCk0sWUWQ7kXSdiLAArAJJG2dcJxAMmWPFGCS6UJGpi6QrOeYO0SSU+y4CaQ0vUdx5Lj3iCCI5DQ0NOC9994zE7SXL18Oznm3Rs/2RBxVjhjhi8Q2zjnZmiE0e4ebPdTiSENMdbW9azjNDYswsoomLlWMKg6AS20SVZswioZjAzo6hVFUEy9GLo7hLTJFUBJRFCeebOLImFDWEqbUxZEMawndsqMDqgjaxJEwxZFilnNuyTnQhRJTOLjQhJBVJBnhNq0OoU+lJsCC0NoMLYwm9XCaKZB0z5F14EkGgEmJqrI8cOieI1PYWARSF4M9JvQeWc59yt6fJNtbr1c/4Kfngd9sJfxLU1MT/vvf/5piaNmyZZBSYvfdd8eMGTNw88034+CDD0ZpaWnadXsijoqKiryoJuMwxsjWDGGzt6s4fg+8RmmF0yx1mcuFNpZR3yAAMHvSsXWka4sgMvOMHLlFRuIzAC0ZWi+TQpjhMFMkhaNal2KHGDJEkLEuAAhLmdDrEeEoVN1Hwy2eIQBAJGp+1nqpacKHcw4eCti8SUoooNmglyuhIFQ1DK53LY7Ny8bBEDbzj0yhBKNzm2rLQYKigEmBomDADKsxKewjZDvOZyLvkW30bGMbj71Hvr6/chy/2Ur4l3nz5uHpp5/GxIkTMXPmTFx77bWYPn16wt6S6eCJOFq+YgXGjR2b9vDc2UZVVVSvWkW29hQXr41m72qMGzsGAc66XD8RqU1Om0Y4zSGMNOHSieXbwphQzKDovdVcQ2lOYWQJo1m9RWok5kFyeoqcosgQU4CRkxQb/8j0Fqkx8RiJamWRsIAq9HnW9AHkzFAa18NniuYdQiQKHgxAKgqEEKY3iQcDUMNRMxeJBwOQQkAJBiEQNcu0fGgjzBaGDITAouF4gWRJ0pYRQCgBLK9rwcTyIgQC0PKEgJhASiW8ZhU81uRsxzXSE+8RYL9ebfdXjobWcvp54MBvthL+5bLLLsOdd96JQYMGeV63J+LID102DcjWzCFMz06SB2IqvUNS9RolNsS+H10cmT3MoHtnBCClSFkYOcNoVm+RahFLVlEk9HViwicmiLT1pekpkvqUIcIqjvRlkc4oIlE9dGaIIx7zJAmFaWEyXSgJRE2PkuAcPBTU8ossniShCiiGx0j3Iglo4s0MsyEFgSQMEcS00cSFCimYNhWJsV5PwmvGOfTIe2RcR368v/yCn2zNNtq4rJn3WPGd4BTsscceGaubErKJzNKdHmrOZekmYVvWtYXTrMnUkLpAiVp6nqUnjAwPkuEtMpfp7yJi6cHmIoikkDYh5OY5MgSTjAhzXenwHKkRAa4wbf4xF6FkeIpkMAghNEHEBAdHAKrFYwTAFEhGT7iUBBKgPUkYB4Se6C4YIHjibvkphNcAZNR7RBAEkQgSR0R69LSXWqr1O/bTZRJ2CuE0c0JY04skzYENbeLJRRg584sMYaSGozZvkSaMYknZwlymxgmimFCSsXwjYfesGWG1aEcUEUu4kvOYQOIKg9QFkVMoyZCid+WP9UyTDo+RdSgAQBNI1lyoOIEkVE34GOWca6NvyzDMcWWFCin04QCs4TVn9/5EoiUd71E3SOqFJDFFEDs9noij0VVVvsj655yTrRmCc44xVSOT25skETslr5G1HqfXyG0fLuE0GdHmQRtbKMGi4di2zpGvXYSRtTeaVRiJiCaKrCE0VU/MNkSRGrH2TosJIiGkPbRm8yRp8wECQKS5A9G82PxAxsSVmmdIm3fMTSgpqrCJJABgetI5171IHAEzgVw7bLE8JAObQDJsCECfbkRLUudKCGP7MrBoBAiFYj3eDP++2QstfvTsHnmPuhFa8+P95Rd7/WYrQbjhiTjqzqRuvQXZmjmCzvlsuutlcvMaJVvX6jXSyxKG0/SJYAOIzZVmTJ1hrguYywyvEACokYgtv8gaRhO6N8kaVlPDqk0UqWERJ4ikKm2CyJl/ZCSMqlEVUclseUYAICDMWb7dhJJmtyaSlJCiC59A3NQCRpd+ax6SAj3EpnCt+75QtLnchKqNhQRD1IR0L4+qJeMLQKpG3zqY4TVb7zVncrabpyaZ9yhdXLYLZmHyTy/x0/PAT7ZmG8Zj93Gm90N0H09k84qVK32RgCeEIFt7QhKRIoTA8upVie1NxWvkyBdy3XfcSNemAYgb7NEZTtMFjxqNYnmLPkO4dQJZ6/xh0bCtV5oajhdGIhxFtCMM1ZgbLWx4kFREO6JQI5oYim6Paq+OKCIdUfO7CBsCSkXEWGa8jG0iWpuiEWnWYdQT6YhCjahQwypEOLYfox41rCK63RBsAtEOzTZVt1Wbf60TUX3+NbvYi5qT4ZrHIRp2D0HqwlMIFd82CKj6kAjaxpZzYM0J05Ozrec35glMkLTvcn0knXMtSfJ/l/dXpsPHaZKTz4ME+M1WYsfg73//O2bNmoVdd90VEyZMsL3mz5+fdn3++utE5Cwp9yTrinR7qLkkYdvejXCaOQ2IIZpiuTG2H/lEwigSL4zUSNRMujbFhu4tMsJnxnerl8iae2QLs+kPaltvNf3PX6RDha6TLL3VNO8QU2KeIqbqSdkQEGauEde8RgqDUKXpRQK0cY8EIrZDaiRqG94lay82498UC0LLKbLmH0UAIBDL5VK1MZcgVG3MIpecIdObpDXI9RQnHPeIIAgCwMKFCzFnzhzMmTMHxxxzTFy4dOLEiWnXSeKIyAzpiqXueI1MAZTca2QO3qiH1DSPBddzixx5RsI+F5o1+TodYaSGhenVsYoiq3AyBFEsQTuWqG02XXeNy4gwk7Vj04NIqBHoCdh2oaQEORAGpKLtVwgJJahACQEqtLCdOX5jAoFkHZNJCQUhuYDUJ62VKo/PP1IUQEr9OHMwYZmSxJmcbenaDyUmepKOe2RcC0lG0E4KiSoiB+B6L9KM70fdea71RYsW4fLLL8ctt9ziWZ0kjojU6IlnKN1EbMA9EduljlS8Roa3CFaxJHks3GNZLy4B25l87RBGWkhKC40JVWqfdZFkCCOrKFLDIk4QaYnesdwjYTleRg+1SKeKiC6OONOPncL0BGweJ5Q0r40mkjTvkdRfmhcJIQXRjigUXaAF8kM2gcQ4tyVpG3Oymd8BM/8IgkMKBWCqNsu5EIBQYsfVyFOCnpydyHvUlXCxzrlmoSeJ2UkhMUUQvqCkpAT9+vXztE5P7vwJ48f7Iuufc062ZgAmtVGYJ44b2zN7U+i+n6yHWkKvEWDzGnEAE4Nt4C7hNOscaKrFM2TrlZaGMFIjqpnrEzVzhLRebGaOUKeKcERFhyrQoQpst7w6OrX53Do6w7Ey/RWOqIh0qpYcJtX0WDn3aQ3xaTlKms1qRNXXC5tjM6m2kGLUdixMr5plCATjGHKhYmJ+J7jVSwdLSBNwzz2ynn+3fDKnCHa5VtLFuF6zMBafJ/jpeeA3Wwn/c9xxx+Fvf/sbmpubPavTE89RJBJBXl6eF1VlHLI1c0SiUeSFQt6G1Mxy6S6ULD3UbO/JvEZCRVgAeUZPNUs4zdZlX/cSAYgTRmo4GieMInoStAgL01tkFSFWL5EaFVClhCphvhuoVs+RjL2Hdc+R9QddYRIKY1AEoEQZlIA0vUlC1UJpRghPCXL9M4cQEkEACCnQAm2AyqNmiE01JrJFwDwGjGuT2Ro92KzhNXAOyRREVE18MoW7eo9cc48SjZqdyOvjUWjNvF59gp+eB36ylfA/H3zwAWpra1FVVYWpU6ciPz/ftvySSy7BzJkz06rTE3G0pqYGE8aPz/l5dIQQZGuGEEJgdc1a7d+4tQtpJkJqLh4la73JvEZa9SrWhPMxXrRoE53ong4Rjk0BIiJR00tiG8fImmOUgjCyruMURYbYsYojQxgZ37frImU744AqdWGkCSJAE0qGWFKYREhKm0jS2u8QGOHYR6tAMsZOUkIBiLAWYjPma5OKdhy4fi2KcFQTS3r3fhmNQDAFq6MhTOwTNb1HEFybp03v2i+FAsaVBCEw/ZwmEzsehdas1yvn/ri//PI88Jut2cYYeiMb+9lZ6NevH0455ZSEywsLC9Ouk3KOiK7JRrfmZCG1VLvvA/YcIvO73WskRSw0Z5QZYghAfDgtbB/XyEi+TiSMtG70wuYtUsMCESHiRFFYWIVRvDjq1J9vnUJaxJGLKOIMAMN2VSLEASWiIqgnZJpeJD3nKJAfcBVIalg7bsbcbExRTBGkGu+RCBQETbGkcEX3HkFLbGdGT7XYyNmmx8g8H5Zxj9JIzPZszKN0oLwjgsh5Zs+ejdmzZ3taJ4kjokf0uAt/KiG1rvZryUOSwi6enF4jUzwZHi09CdvaO80Y6wdwCadZeqWZOUZJhJEaVqFGhS6CYmE0QxRZw2qqw8umCSntc1hIBGzhNz2cxgCFMahSmiIpLDThpEqBUKeEEpBQQgpUGKIxahNI3DFYHFOiUBCAiMS8R4oSgmpOZKtq045w7dhxrljCZvrcaopiHn8Ibh9A0uo9ciZmd2e+tB4KmLT2SxDEToEn4shPSW1ka+ZQjHwSdO1K9ySk5uY10t/jxjVyDPjILV4je6Kxw0Okz5VmzJMmbN31DZEUC6UlEkZWcWQII6MMcPcaAXZxxFR7zlHMe6QJpRDXRFKI2z1LIX1+tkQCSVVivd9UAFxR9fwiAclVUxQZ3futoTapGsdX2ylHbLoW67xrtnGPjHOlcLv3yDi/QM9Ca12h70Px2f3lp+eBn2zNNkyfDDob+9mZqKurw80334z//Oc/2Lx5MyorK3HSSSdh3rx5cTlIqeCJOJo4YYIX1WQcRVHI1gyhKAomjh/XtfcnSa6QgVvPJNeQmnVbl0TsRF4jLgUmYKu53MwzsoggaXnZxZKevBwWsZ5fjhwjqzDargqbtygsYp+BeM+R0UJDKHV2aiUdnRFIxqEwhojUupkaAkjLP5J6SI1BlUCIay9jfwXGebIIJKaLIiOcxhSBQAGHGlHN6UiM8JpUheYpUgWYkW+ke4+k0KYWURSJCawRTAb10Fli71GixGzX0BpT7GVdhdZS8CSZ16tP8NPzwG+2Ev5ny5YtmDx5MgYOHIjTTjsNAwYMwNq1a3H//ffjrbfewptvvpl2nZ6Io9bWVhQWFoJ1dzyRLCGlRFtbG9maAaSUaG1rQ1Gfgpi9SaZv6LpCl67eOom6ddumCnGtMuZFalUVFIoOzWPk4jWSQpheIwBmOM3ssh9RY6NeC5lUGMU8R3ANrwm4J2UDsdSgsASYlLAnY2ufucVzFBZGXlLMixTiDNtVESeQjIRtrnBd4Ollev4RU6IIKCGte7/+b9f0GBnHzJJ7JFSOdsZRxFSA66Nnu/34OENrFiHj6v3pyVhFCeowr1cf3V9+eR74zVbC/zzxxBOYOHEi/v3vf9sE72WXXYY99tgDH3/8Mfbbb7+06vTE71a7fr0v5qgRQpCtHmIVKUII1G74Lj17u5NvlDAcFxNFiUJq2uYCQgqsZyVQhSXZOonXyEjMlkKa4TSpSm1utIgxtpHeG82WYxQTRmEhdbEU+94hJCKW71YRZWwb1cMTUc5t5dZXRNrrUaW2L2ed21Wh9ZYLG4JP1fOotJwpQ9jZ2xq1HQ/rMTKOmTHukRAS62URVItIdT0XLucspXOcbL00c9+c12uXkxv3Mn54Hhj4zVbC/9TU1OC4446L8wQOHjwYBx54IGpqatKuc+cKShLpk80fhmQPqmQDP5rbdx1Ss4koy/6sU4Y4vUZSCNNrJFUJIaQZTtMEkYh5lKIiTrw4PUeaMIoXL1bhZIgbY1TsiLALHmv+krPO7Wr8MpvnKmoZf8mwXRd9QhhTnehCST9GUtVyj5zHyTx2wu08dHE+dJINCJkQ+lEjfArjPGuvnYWKigq8//77ceWtra347LPPUFFRkXad1FuNyDrJ/qW7LYsrc8k3kl38WEqnNwNSTyZ2+bF35Bo5vUbmfGlx4bSYZ0gTL/HCJGIpt4bR3AaD1JbF3pklaTuWbwQYITSFAeDQ8pYEzDCbgcJg9mTjYQGmcDO8xhVmeo4418ZhkQozvUcAzNwjBGEmaUtVmO8Q+vQhDLHQWaLQmn5O4qYTseYdwTq1iGIvSzZJbRpJ2QRB+J9zzjkHkyZNwvHHH49TTjkF/fv3x7p16/Dwww+jrKwMBx10UNp1eiIt80KhnI8tAwBjjGzNEJq9weT2ppCMbStLNCp2ou2T9FLTVtXKmBAIyTCQNBE7lmtkThKre42k1dOiqxc1rEJYhFEs+RoJhZEq4z078cdC2t91nJ4he0+4WJjNrXec5pGKhdcML5GRQ5XMe2QcH+27PbQGoSJPRsCkavfKJTknbteAq3h29mZLdA0kK7Puw5f3lz/s9ZuthP8ZOXIkPvjgA4TDYVx44YU48sgjce211+KAAw7Am2++2a3Ee088R2PGjPGimozDOSdbMwTnHGOrRsUKMpHomEK+UcLllnU4JKo66yCgJUPHJWVbv6silptjeIx0r5Exd5rQy+35QrB5kNQEwshVENlMVy3v8f9ljLoML5LhLQpp4yxClVpvNs2DxPTxj7SX1EOBgDZhrdkmF++RmXwthDb6tSUxG/ox5ELFaHUrGA9ajrveay3ZuXHrcpyJwRctSdmcc4wdXeVt/RnET88Dv9ma9X0q2mTQ2djPzsTuu++OhQsXAgDa29vRp0+fHtXnydFraGjwRWKbEIJszRBCCDQ0NnbP3lRCHD3JNzKW6+sIoaKRF0K1CCCz6rjEY7vXyJprZHiNhKp7YmwCyB5Wi3RDGAEAMwZI7EIoOOu17tNpj/E5IoStDUbukdN7JM3yxMcLAFRVoEGG9LCec6TybuYddUU3w2M9ul57AT89D/xmK7Hj0VNhBHjkOdq4aROKi4u9qCqjSCnJ1gwhpcT3m35Acd++KW7QzV5t3ahHWn6MpapCCIFNSilGq9vM8JlbSE0KTSBpy6XNa2TNNZKqdbTr+JcAuiWMAH0gt6jxnrytWp1G3Xq3foXZQnvaaNp275FUZVzukSGMuH5suEtoTagCPKh5tZjKgSDDJl6MYrVB/9cV1PKKkuQd6Qc6sZcoHQ9SGutq12td6tdrL+On54HfbCX8yd13341Fixbh17/+NZYtW4ZFixYlXPfXv/41Zs2alVb9lJBN5Aap/oNzJmPD3uvMSly+kW17aVkvcUjNSMQ2xAAAm9dIqgIiLmzWs1BaTzBEUIgDhkACBxQZm2YkNr0INNvDKgIFAbNdStAhFpOF1vQEbeNYmMdY4ZowspwLrfdMMGasdbwjIGFSdkISjJRNEMSOz8iRIzF16lT079/f/JyI/v37p10/iSOiW/R4TrVU6jRGxk4Fl2Rs6zJ7tcIMKMd1Q0+CLbwkjHGBjHCau9fISMIGYmWZxtiPJoAM25irfWEhkW94xJSYCGQqM0NrSY+J4/jFrS1U2AWRkZRtmUpEqyjhYJDp9ljrLjTHGpEVsjR9SEp/MHzMySefjJNPPhmAlli/7777YsSIEXHrffbZZxgwYEDa9Xty9PwyyixjjGxNh3Qmgk3R3i7FTjdGxk6KS7I2A9Anuj1+113kGyXC3iXf+bJOEdINZZSgt1pXJNq/9ZUqXeUdATCHRSgUHVoYzV5BWrYnJFmPNQupCOq0769e7vqfE8+DFPGbrYT/eeCBB/DOO+8kXLZ48eK06/REHFVWVvpiokHOOdmaITjnGDliWGJ7M/XjkuoPr2VgQg6JYR0/gFm68DtJlm8UE032kJrVM2TkGvXUa2TvrZY6dluMKUrsywy7hdTb4mij0U5t/9ZxoFSHiNTKOSSGd2wGN/xH6Z6bnpBmd37teh3uq/vLL88Dv9lKxFi4cCGOP/54TJs2DfPmzcOWLVuSri+lxNtvv41TTjkFU6dORXV1tet6jY2NuOGGGzBz5kyceOKJePvtt3u871TZsmULSkpK0t7Ok7Da5s2bMWDAgJy/0IQQqK+vJ1szgGlv/36p2+tVUrbbj6vLiM3m2EWqQH2oBGXhrbHqHcnYiXdl76XmFEWAXZQY793yGkHvpSZj7+lg2GbkGmld++3d+c2hAMzk61jeUboIVWBbQTEGohNcVbVcImtYzS18aUxC60YmuvMbuxUC9du2pXe99iJ+eh74zVZCY/78+TjllFNw6623YtKkSbjzzjtx8MEH4/PPP084q/3Pf/5zrFixAocddhj+8Y9/oL29PW6dzZs348ADD8SIESNwxRVXIBAI4J577kFFRQUmTpzY7X0DwL333os333wTX331FZYuXYrnnnvOtnzbtm34+uuv8dhjj6V9PHp85XZ2duKWW29FR0dHT6vKOB0dHWRrhujo6MDNt92RNXtdQyfW7uJJ6IiouGPBe2jvCCddDwCcydjJMISG9jnek9QdBGe293RweopidqVmjC2MliSsqK2roiOi4rb576IjkmzyX5dhFnQykceWiI6ODtx8622+ur/88jzwm6033ngjOjs7e9uUXufaa6/FBRdcgF//+tc48sgj8c9//hNr167FM888k3CbO++8E++88w5+/OMfJ1zn6quvBuccCxcuxI9+9CPMmjULCxcuxOjRo3u0bwAYNmwYdtttN5SVlZmfjdfuu++OE044Af/73/+6NX2IJ+Loscce88XFRbZmjs6O7Xjs8cczb2+aHhhnsrUUKjqjUTz+z38hHLVOnOreUy1RndYu/ABsgsMIY8W+p2WyDVV3F6npuo1c9m23yZ4oHgsbxucTGSQ7VgDQGVXx+IuvosO4Bpw9BVMlC92rOzs7s3O9eoSfngd+s/Wmm27yha2ZZNOmTVi+fDmOPvpos6ysrAwHHnigawjMoG8XQ2FEo1E8//zzOPfcc5GXl2eWM8YQCoV6tG8AOPXUU3HPPffgzjvvxF133YV77rnHfN199934zW9+g9122y1pHYmg3mrEzoEHeS3W/Bo3uhs6y0WMHmsEQfib5uZm2/e8vDybUAGA9evXA0Cch6WiogJr1qzp9r7XrVuH9vZ2jBo1CnPnzsXXX3+N4cOH44ILLsCMGTM827dVWHmFZwFhP2T9GzaSrd7jK3tTCJE56apLu+tuPBBL1uk5eoLVS5QOyXrpJYJ108vlSoZCbb66XuEve/1oa1b3ybWu/Bl/6flew4cPR0lJifm6/fbb42yKRCIAECeaCgoKzGXdwfDI/fKXv8TYsWNx6623YsKECTjssMPw8ssve7bvhoYG7Lnnnti4caOt/I033kga8ktGjz1HUkowxtDS0mKONsoYA+dcc71bfiDSLeecgzEG1ZEkayT5OZPpEpUrigIpJVpaWhAIBNDS0mKu31MbM9Wm1tZWBAIBtLa2gjGWsE3Wcs9tV6MJ17fNVcY52trazGMrpQQkwI18GSFtU35wzgApIKReh9S6gQeYFvYSUl9fSjApoDBAqBFtn7qwYSIKhUkINQIR0ZbJaBSIhsFEFCIS0SZFDXcCahiIdIKpKtRwJ1q2hzVbO8NaL66OMKKqQDQchYioEFEVajgCNRJFVAWilkljo0JFVFUhGEeUM3RKhjCAjqiK7QCiAY7tKhDhQJgxRMMqInq5iZTaqNLMMd6JS3lECkAF2mQYYCHzgaeAgQsJKQW4ophzhgF6+EsvZ4o2yZrCAK63gQcCUBkDOIPkDFEpoAqJAAuCMyDAJAJSQolGEYgCQVUBVxkCUYFAVIUiJThjUDgHF0CAMSgS2C5U7VmwPQyEOsEUBTwiwQMqZFhoo2QHgmBKADwQgRIKQjAOKEHtBQYoAXDGoDIOyZiWkM0DAOfgXIkJTsYhGdfayBSoUkD7r6ePjaSPoeTUdsZ8U9ZngZTSvJ+s4jHu/jCncsn+M6K1tdV8d47q3NVzL6PPCJfytrY2KIpi+03w+lnuVZuM34IdeaTsDRs22EYrd4oQIDZI4tatW23l9fX13RpA0VnvySefjF/96lcAgIMPPhjLli3DH//4Rxx33HGe7Puxxx7DkUceGed9OvLII3HjjTdi6dKlmDJlSlq291gchcNhSCkxbvz4nlaVNfxk69hx43rbhLQYu8vuvW1Cyux53Z+ytzM3B4gEEE2tfD5+0MrdooOJIoZqgmWJ8mR/SFCeJhN/ebc3FWWBsRN37W0T0sJPzwM/PWfD4a47Z/iV4uLiLqdyGTNmDPr27YslS5bgoIMOAqAJxiVLluDMM8/s9r4HDx6MoUOHYvDgwbbyQYMGmeE0L/ZdU1ODCRMmuC4bNGgQVq9enX1xNGDAACxevBhjRo+Gov9by1XPUSQSweo1azBm9GgEAoGc9hypqorVa9Zg3NixUBQl5z1HQo1ixaoajK0aBUVhOe05ikRV1AQGYcS2tUBnZ8xz1BGG6AxDRKJQ2zugdkYRjQLRDhWR9gjUsIro9jCi26MQgiPaEUWnKhAWEh3hMLYLIMq59l1IdKhC8xxJrdwkDc9RNMDwdEcNTuXDEZRI23MUVDiCuucoXwJ5DMjLCyDAGAo4Q77CEZICeZwhUJQPHmII5CsIhAJQFCDYJ4hAYQg8pCCQF0AgPwhF4eD5ISgF+eABvSwUBA8FUVNcidFiCwKhPM1zFAyBB0KQwTyH5yiUmueIB3Tvkbeeo0hExaqatRg7ugqKwnPec2R9HjhDQbnmOZJSYmV1te03IVc9R9FoFMUlJV0mFnsJ47GQV6b3kyrBYBBnn302HnroIcyePRvl5eV49NFHUVdXh3POOcdc76qrrsLWrVvx+OOPp1z3xRdfjL/+9a+YO3cuBgwYgPXr12P+/Pk499xz09p3MiZMmIAFCxZg3rx5tvvjhx9+wPvvv48bbrghZXsNeiyOGGPo27cvysrKzBshV1FV1Xe2lpSU9J6tSfI9nN2u1WgEffsWoaxMt9fpptbXj82+LiyjYWviiNnKZGz6ECkAEdU+6w9XJqJauRqBjOriKBKBjAa179GINlhhmANRBTIagIyEIQPaD2NRsAAl20OQTCIKQESiiAoBVRdn0VAQUcGgShVRLhAJcAgBhLmCqCKhqgJRIaEIiYCQYEwBIBGOSjChDaTIBBBmHExKl0lj9XGLuizXHnBFPIBAVFg8QTK2XJWW77CVB6VAiDPzlc8YQlFt7rUCAAVMIsQ58jnXQmmSISAZAowhkBdAMBhAQOFQFI5AgCMQUMBDASh5IQRCAfBgAIG8IJT8EFgohL6FfVCm5pniiIXygUAILJSvCZZAECwQBAuEwIJBgCtgAV0cMQ7J9UeSomhTeejiSDKuiRPjwWeUcR4bC4nFPktrmRV9e+3+KkJZWant/ko6fUgvTi2SE8+DFPHbc7awqKi3zcgJ7rzzTqxfvx6VlZUYNGgQGhoa8PTTT2OcxVu5Zs0a1NXVmd+fffZZ3HvvveawDT/96U9RUFCAyy+/HKeffjoArSv/2rVrUVVVhWHDhmHdunU45ZRTbIIllX0n46yzzsKdd96JQw89FOeeey4GDhyI1atX4/e//z2mTJmCyZMnp308qLca4S8YS6urN+PcJhu0SU7t/16ZwsFUrv2b5MnnPTISHZlit0Fh2uCKhkjJxaHvrDZp9sYnoxrJojzZMeDaserynynv5g+jDxJ5CWJHo0+fPnj55ZexceNGbN26FWPHjo0bgPGuu+6yJUkfeuihGDt2bFxd1jnOAoEAnnjiCdx5552oq6tDZWVlnKculX0no1+/fvjPf/6DSy+9FHPmzEEkEkFxcTHOOOMM3HXXXSnXY8UTcTRwwADf9EwgWzMD4wrKB/TPmr2S8fhBAzkH4wokkvdwYJDo19kIReFQFQ631TURxMyeH671KAyKwwSrSFKYUQZzVOp0MYYOSDaEQCKM/RqfY/axuPWYwsAU93OX7FgYZVzRPGcDok1xwspVRLmUZXPSV8YYygcO9M/95aPngd9sJexUVFQkHDSxqqrK9r28vBzl5eUp1TtgwIAuJ4BNtu+uGDduHBYuXIhoNIq2tjYUFxf36Pz2WBw98MADuPPOO21lJSUl+Gzp0p5W7Tmcc/NEfv311/jJSSdh8ODB+M+77/auYS5wzrF8+XI88qc/4dtvv0VZWRmOOfpo/PKXv0xLUWeLtxcvxhNPPIlvl6/AgAED8JPjj8OF55+HYLAb81C4wXjiMJ85TYWxqkMgcQVABExRIKMRRCJRvPPRB/jLu5+htr4Rz593LKpKkucccIVDQIArDFxhUCMAVxiUKIPCZJwQURhDRBoCyZiyI311JPU2SzOnJj1iYg02UWTY69RDRvu0z6nNHt7aGcaCT5fjrx9+ibqmVvzv7kvRr3++UaFtXcYV3XsH1+WOlbvcd7qsqVmLBx96GB99/DEY49hv331w1a+vxBBHwmguEIlE8H//93948aWX8N1336GyshJz5szBCccf39umJaWurg4/OvpotLS0YM3q1b1tjiuT9tgDbW1tAGIC6ZprrsHPfvazjO9b+0OR+XAjUzya8NlnBAKBbs2lFldPTytobm5GaUkJFixYYF5kuTqfjhACGzZsQP/+/XHW2WejoqIiblyEXOHTTz/FnXfdhbkXX4yJEydi1apVmHfppVi1ahUeffTR3jbPxr/ffBMP/PFh/PjYY3Dj9b9FdfUq/GLeZVi1ejV+f6/ec8lN3CQTPKnCFfc5uzg385Oc/OqZ17EtwnHi3rvg18/9GypiHhCmKEAkqoWOFA41ogmiRF4VA02ESNNDZAik7oqiWPMUQDXe06vHEEOGt8gqiAz7jOU8QftsQonHkp1jHiOOnz2zEANLinDslIm46aV3EEk0NlImnwtuQsql7OTTzsBFF8zBOWedifXffY8/PvQQjjjqaHz0/nsoLCzMnH3d4ME//hF1dXW49pprMHDgQLz40ks466yz8OSTT+Lkk07qbfNcEULg3PPOQ1FREVauXNnb5iRk48aNuOfuu3HooYeioE8fAPDkB5XoPf7+97/jqaeewvfffx+X+H/77bfjhBNOSKs+T8JqXFFQUVGR88l3Ukq0trXhtttuw4wZM1BWWopn/vrX3jbLlT322AN33303JowfD0VRMGbMGHz11Vd45E9Z7H6eong5dOZMHDpzJpavrMbYMWMwYfx4fPfd97jupt/h3rvuSO+6MPbJWNoTrbqie41M7xJX8Ps5P8aa0FC0f/1xWlUxhYGpmlDiCoNUODgT5sSu9pAaA4eMEyRph9bMBGSGdA6Ic78c8WLJ+MwZ04WO1jYthNa1IDR4as6PkdenAG8uX6cVGN4g53siUs1NsiRjd5clH70PRVGgqioCefl47E+PYPyuu+ODDz/ErMMP73a9meDSefPMP5qqquL444/HO++8g7fefDNnxdGdd96JvkVFmDFjBpbmYPTASr9+/VBRUUEJ2TsACxcuxJw5czBnzhwcc8wxcQ4aY4LbdPBEHK1duxaTp0xBQX4+pk6dimuuuabbccNMs2jRIiz59FN8+MEHuOeee3rbnIQ4T+62bduw6N//xiGHHNJLFtmx5vwYPzZWItGI1uXb0Q7XXKFEyxziTDIOhsTLmaJoI0lzh8fIEEg6gYD9so95RLjNIyJMEcTAuSGKYqPPMkXa8o7sHhlNIAlLeYgDYSF7NNdaKmj7YhaPkdVzFPMgGesyUxTF2s5sbXa03RJuY5xDMY6nW3zfTfhwJT6swOKvk7SWp7jMKdQjEW1AqUAgmHM91Zz3TnV1Nb799lvMOe+8rNuSCh98+CEef+IJfPD++3jq6ad725wuuebaa/Gba67BqFGjcOaZZ+Kss86iHCSfsmjRIlx++eW45ZZbPKuzx+KoqKgIc+bMwRlnnIGWlhbcdtttOPDAA/Hpp5/2aGTNTLB27Vrcc889eH3hwpzM23Hj9DPOwJL//Q9b6utxxKxZ+HM2PUfdpL5+K/7w4EM4+Scnpv6w4dw1PJZMTBkwziEdeUfaD7DQZoA31jH2A8T9kLv1WHMmIifLO9KED6AwiRBn2K5q76pqzUfqeZgtFZxhNA5NLGnL4BBJ1hyj+Hwj5zGw9lSLS87W92EcY2siNlMUTShZf/BT9BhlMlH7hpt+hxEjRuCA/ffL2D56Qnt7O3afNAkdHR1oamrCTTfeiDPOOKO3zYqjoaEB5557Lh55+GEMHDiwt83pkmkHHoiLL74Yw4cPx5JPP8Uvf/lLrF69GjfffHPG952sk4fX+9lZKCkpQb9+/Tyts8fiaN68eajbtAklJSXgnOOF55/HxF12wWOPPYarr77aCxs9IRqN4pxzz8Ulv/wldt8990dxZoyhYsgQPPjAA9i+fTu+/PJL/Pqqq3DppZfikUce6W3z4mCMYeiQQWhvb8fJp/8UAwb0x523JlHx6eQbWdc1conM8BtH4iGioYkkrs9pzxVAVcE5x+DINqw1h8KJCaWu8o7cQmtKQEKJaDbEco8071GIM0AAqi6KDJESTnHOsnR7qxnjGcVsYboXCZbPzFw3WUgtWb6R9XhxY/DXmNWm8GGcJxVBzDlOEWAXUMmEUQ9ymBhjeO7ZZ/H6okV447VXkZ+f7+WMcJ5RUFCA/7z7LlpaWvCv117DLbfeihGVlTkXVrt47lwcc8wxmDVrFoQQKM3x/J358+eb0zJNmToVnZ2duOKKK3DNNdegoKCgt80j0uS4447DxRdfjPPOO6/L0cBTJWVxtGjRIsyZM8f8fv/99+Pkk08GYwxlZWVmeVFREXbZZRes6MVkvLq6Ohw4bZr5/awzz8ScOXOwdOlSbNy4EY/po3u2tLSgvb0do8eMwUN//COOPPLIXrF3//33x+YtWwAAe+25J1588UVwzm3HdeTIkQCAU087Dddffz2GDBnSG6biggsvwjuLFwPQwlPV334NQAsB5IVCOOHkU9HS0ow3/vUKilKN5acilKzrJBvrSO/ODy5w/wsv44Hn/gVAyzd79ca5mDhsIHg0gjJsxzqzak0ESb1bf7qhNWuvtRBnpgjSPEmxkBqgiaJ0BFI6vdUMEWR8DnGGILOLoVjITRdPIZ52SA2AZV1LKNIQZYZ4svVK47GeaqmKmlQ8RixFIeXg3vv/gIf/9Gf88x8vYJ+99055u2zDGMOwYcMAaHkT62trcc/dd+ecOHrttdcwoH9/czLR7du3AwBGjxmD31x9Nc4///zeNC8OZ+eh/fbbD9FoFKtXr/bFn2fCzgcffIDa2lpUVVVh6tSpcZGhSy65BDNnzkyrzpTF0SGHHIKPP44lsFpdWKtXr0ZVVZU5JHttbS122WWXtAzxkoEDB9q65xcVFaFv376oXrkStbW1qKysBGMMDzz4IP75z3/i3cWLezUE+M9//tPM2TEmBRRCoKamxjyugDZQFgBzNNLe4I7bb8N2ff/W4RXb2trwo2OPR2trC97416vaeBZeh4/ccpCk0MM19ilNAOC8Y2fiJwdPBYSADHeivG8BABWCB1CT1x/g3+vVMlveEVe7Dq0pQQ6pckghTO9RSMpYOE1KizDSvEdwEUiqTJ6DlEpvNatXCLALI6cgsq5j9RopIQ4lyPV9dhFSs+QbMUsITRpTPmiVGA1I1jhzeWxE654nXXfFPff9HrfdeRce/MMfcPBB07reIAcwngf5BQVo14VHLrFyxQpzig4pJR57/HHcfffd+M+776K0tLR3jUuCMQ1JTU0NAHgemnGD8/hczEztZ2ehX79+OOWUUxIu705P1JTFUX5+vvkPxsq8efMwc+ZMjBo1Ctu3b8cNN96I77//HrN/+tO0jfEKRVFcba2oqEBzS4vZs664b9+E62YTNy/QU089haiqYujQoSgoKMC6devwu5tvxl577olRo0b1gpUaVhFp5AJ1dHTgpFNPR/3WrXh70UIMHJh8oC8baXbnTycpu7hvX/QNBfV51yJANAwZViE5R1gGAF0oWLumMzVxl34lpAkioXIgjDjvUVDlUKVAWMQ8RYAmhoycI0MgGd4lVUJ/JRBJSXqrOXOHrCIpaMk5sk4fYg2tuXmNuC6SknbhtwhHM6RmCbVJsPhwmuExSiEZO2Mwhvv/8CBuu/MuvPjc3zGoYmhOz8Z+/fXX47TTTsPEiRMhpcQHH36IZ555BhddeGFvmxbH0KFDzc+qqpp/5Hr72erGa6+9hqamJpxwwgkIhUL44osvcO211+LII4+0tYPwD7Nnz8bs2bM9rbPHOUfTpk3Dr371K2zduhUdHR3YdZdd8Oorr6Q9Ay5h5+CDD8avLr8c1113HRRFQSQSwQnHH4+bbrqpt02LY8Err2Dxu++ipKQYBxw8HcySffLBf97B4EGDtC+6kOmyxxoQ686v+6dc17cII9ekbOhiCbDlHf1l0Ue49YW3IKPaTNwnPvA8FMZw1ax9cfKksWAivteaEuTmeEhu3iOEFAhVIiSZLbfIGPMoxHXHj+5BUqURVjOStGMiydjODftI19bu+bEeaoYwsvZYi4kjvTzAwUNKQq8RDylQgty1l5o1pAYA97z+If7yn8/RGdWO/f6X3g3OOR6+7BwceeBU9wHvuGIfOdsikFx7qjnnVHMud27rIrja29vxm99eh4KCAlww9+eIRqMIBAJgAG64/roezT6eCaZPn46LLr4Y1dXViEajKCwsxLx583DlFVf0tmm+Zp999sHvfvc7/Oryy82yM88809OeToT/YdKDv05Lly7F0IoKFBYWejcicgZQVRUrVq40xw5qbm5Ge3s7Bufg6LiGrWPHjEFbW5st/yirpDD5bHt7O+rr67VZzkdVmt4ESIkhgwfbu09bJ6B1m4Q22QS0+mSzXU5Aq6raxLPRCGQ0DBnRvUZ6WVNLK5a2hlDVuQnoDENEoxDhKIoUjnzGIMJRqB1hRDs6ISJRqOEo1I4IIh1RSFUguj2KSEcUIiygRlREt0ehRlSoYQE1rCIcUc0u+9tVzZOkfZemKFKlRET/7vQaWQVSJMDxp3ANLg5VIV9Pyo4f6VoTPUHmnoAd4kCBwk1hFOQcgYIAmMIQzA8gUBCAElTAQxzB/ACUkAIeUrTP+UEoxgSz+XlQ8kPaxLPBAJT8EJRQEC2RKLZLCREIoSZQjtFKC5RAEAP6laKgsAgsqE80GwhqE8/qPdeSTjirTzqbdMJZ/bs1oTuZOJIAvtcHfRVCatdr1ShwRUFZaSn6FCUZJb0XJ51tb29HNBrFhu++M59duYyqqvhi2TIMHDDANsdWriGlxNatWzFs+PAu1/3hhx/wk5/8BJdddhl+8pOfANAGkjz55JNx1VVX4cc//nGXdTQ3N6OkpARfX3YG+uaFemx/V7R0hrHb/X9HU1OTZ0nKucptt92GhQsXJlx+7bXX4qijjkqrTk/GOaocMQKFhYU5P0YE5xyVI0aYsdji4uKcvWgMW4PBYO8JIyBp2MvwAPXp0wfDhw9HWb9+KOpTELsOutLdtiTr7iVld5V3ZKIvZ1xFcUEIe4cUFEbLIDo1ASTCUVMMSdN7EoQUQkvWDilQVGF6j5SQAqlKMJWB614ja3gNEJbcIs1DZAgjI5ymSGYRSNYu/jFvkNRzIgJC2LxE2ntMBAUd4bVYCM2eZxTk3AynaYJIMXuoKSElodeIh4JxXiNDBJf27YP+eXmQgSD6KwqKgv3BgroYSkSyfCPjXHdFmsnYjDEM08MmEky7XvXnVq6NcWSlT58+kFLanl25DOcc48eNy7kRx50wxlLONR00aBBOPvlknH/++dhnn30wbNgwnH322cjLy8Oxxx6b3n6pK7/n7LLLLgiHw7ayhoYGvPTSSxgxYkS3OjB5Io5S7pXUyzDGyNYMwRhD36Kink8H0uWO9DCbS96REVpjQGwwSGO8I+ihNb3HVF+okEKx5RnxYMDsMm98NhOzVb1Hm5B67pEwBRIASNXxIAoDemqy2b0/rJscE0OAIgFVD8UJsLiwmuHYDTEg5JgnjcM95yg+z8gujDTxo5jhNK6LPc61EBvXRREPBmyJ2DwY0A93bJnxDq6AKwqKuABTQmbOkW18I+t367mzIK2eoAxiXq8+wU/PA7/ZmiqXXHIJXn/9dZx55pk46qijsHTpUnz55Zc57xTYGTj++ONxvMucg9dffz323XffbuW+efIUWr5iRdwIybmIqqpka4ZQVRXLV1bb7U31oZHsB5Ix9zwTa1jFpQ7XruO6t0JlClagP1Q978X4h8X1hGMlpP/whwKmx0QJBSxeFk1MKEEtgdkQF6aw0D8HObeJkxBnKFDiRYu1d1k+5/q7/srTBEl+XgD5jnXcBFCifViFkZlnFFJsSdiG54hxow2BOK+RWWZJxNaEEIcKhhXopwk7s7eaexf+Lsc3sl4HKeYbJcVxLbperzmMn54HfrM1VRhjeOqpp/Dtt9/i6quvxqOPPpqTCedEjP79+2PPPffE//73v7S39cRzJNwm/sxRyNbMoQrR9Y9VV0nZCUbKNrcFUg+tcSXOewREwDiHEFqPNKYv48EABKKmx8g6YrYMBqGqnVAsniUD4TJWUbQjCoR0caB7kGzhNGaMps3MfCN7zlGsm7+0hMQKLHOduYXW4sYwSiCMAnpekZFn5Aynacu0RwMPBk2vkelFcniNmOERYhyCcVOEOr1GsXOcQkitG4M/Jss3sqEPHKr67P7y0/PAT7amQyAQgKIoUBSl2/lUFFbLHtFoFMuXL++Wd88TcUQQ3SbdvCN9vZRDawAYVyC5CqhqrIu5MbFtIAgmVO1BEtG8RzIUMMcv4qEAhHCKJwkpJKSetwMAUpVQEBMAqh5DYwoHC6tQosJM0jYEkpaDZAijmFAyphhRGLOJI0UYI29b53CDqygyE7MDMW+WUxgZeUZGiM0ZTjPfTW9RfPd9W5d9rgCIjRllDshpnCIjEdvp9XNeD6nQzcEfCaInzJkzB1VVVTjmmGMwe/ZsfP755zmfW7Uz8Je//AUffPCBrSwcDuPjjz9GOBzGQQcdlHadJI6IrkkhKTuj+03UpT/RVCJGl379x1la/8Ua3iU9XGf+YFu8R0zVhIFQBTgCUIwpPISAogsnABCqhGLpdBLdHrUJJABQoULRvUj5qkRECFMUGeMQxZKxmcWLZMxTpr3ncY4CRXMv2SeOtXfpN0RSkHNLkjWL5RglEEZM4WaCtjWcpgQDXXuNgsGY6JEsbuDHuNCmcW6t79weMnMLqWWKXE7GJnKHP//5z1i8eDGWLVuGQYMGYfLkybj00kvx2GOP9bZpOz0dHR1obW21leXl5eGss87CRRdd1K0cOE/E0WjLKM65DOecbM0QnHOMqRql22uJEblN9eEWWnPMnyZFkrGNAPfQGqALIy3EligxW+EqRgfawaPaXGtW7xETmmdECgElGEBUDZuhNhkMQiBihpyCACId0S4FklQEmMIgwiqYyjQvExO2xGy4JGNb21kgBQp0N7lVGBnfbeE1h7eI6WE1pzDSvEiGMDLCaob4CdqSsJVgQMvBsg6YyTlg9EjjCjhXMEbpAOfBuJCaLRGbK45u96mF1Gxd+K3Xgtv1YSuLd6nbr9fcx0/PA7/ZmgorV67Er371KzzyyCPmILx///vfsf/+++Poo492TQYmMstHH32EQYMGoaqqChdddBEuvvhiT5PjPRFHuTy2kROyNXMEA/rllOao156E1izeI8Y5pJl3FJtrzQitgSsIcqF7OjQRhUAIHDDzjRQE9R5pAajhKHgodqtIVUDRbx2je79VIKlhfQwmzsAUoYkirikeDthEkpAyLu/IKo6ievOClqk/3LxG2lQgzBRFADRPkJEgHrSMgB3nMeIIFARtwsgQQ9YkbCUYtHuQAiFbqExyBUFzXrU0ErGRZi81l5BaUu9Pgm3N69Un+Ol54CdbU6GwsBDvv/8+9tprL7Ns8uTJ+Oqrr9Kui7HYqPOZhO3gXs9HH30UhxxyCKqqqnDeeedh+vTpOOecczyr35Ojt2LlSl8k4AkhyNYMIYTA8upV3tvr1mvNetPzWOjF/IE0En7dupIHgxBcwQq1L0QgFNeriocCttCR7bM++KFRpgQDuqgwenJxXXQoZi82c5BFfYBFQ6wECrTyYJ6CUFBBvsJRYL5Y7JWn/cgU5AUt5dp6+QpHKKggmBerz/AWBXWvUKAgoO83VWEUiHmJkhyHuFBZIAQZCGJ5uA+kHmaL8xolSsR2eIOyEVLL2PWaIfz0PPCbrakwbNgwmzAyGDduHMaNG+e1WUQKDBw4EF988UXG6vfXXyei9+gi7whI0iU2SWgtYVmy0JqxLhDvPdLLE3qPADAl5mFigaBeRxhSaINEGuE1RR8EUgkGoCIKrt8u3Mg5QtT0IHFFhRpRYUzkyjmDqmgjZivQhgCQQoIpusdIlZCKgFCZ7rGSZk84xeI6iujeomBQQUjvGWfMe6aFt5hZps0DZxnQkRuDOBr5Rdwc/ZpbBoFUbMInaBNGxjLF0p3fNoaRPvK1WcaY7klK4jVy8xJ14TlKKaTmRhdudso3Igh/Mnv2bBx00EF45JFHIITAc889h1/84heu6/75z3/GT9Oc75XEEZEZUgyPmXlHqYTWkiVmC+HerR8wc49YAEAUWg4SoK0jNUEkuQJmpM/o1apqGIolPGAIJMXSnd8qkIy1jG78hnhRLWE0QyQJXQw5hZJ1/4AlhJavIODQl05BZAgzqyiyJl5b85ASCSOnZ0zzlmnHwPQgBUL2JGyLRwjMmHQ2da9R0kTsuGsgSUgtpS78BNG7UFd+b5g0aRJqamrw+eef47bbbsNuu+2GmTNnuq47efLktOsncUTkFg5hZJuI1rmeuZKjS7/VewSYPdcAxJKzGbR3qQkjc3wkI1fG0ntNgUMgBe23jVUgGWIIAJgqTC+SENImkpQgIFQRJ5Q0c2MqSGF6D7UghyJjXiJjX4Yg0tZRLOXMMuq1Yq5rHewxVWHk7J3mHFTT9BrpXfnBGVggZFvP5jVyO+dJlnV74EeCIHZo+vfvj8MOOwzNzc0YNWqUa+izu3gijiaMH++bnglka2ZgSgATx41NbG+qvdasyzjiB4TUvUdxAspY1+k9svZcg9atXOECE4vC4EIBWMjoNB8Lr8HuvXEKJK292r8/wTlURYGIRMAUDjUcBQBwhUONqPqcawxqWJgiSfMWCVehZO5TF0gBVasvEGQIKAFTCGmHSPMQafboAkkXQtwcyZubAsroqcaDgVh3fUvydTJhxEMBcOvEsUY4LRDUPisKOOPYpYRB0QVUXA81ODxD3EX4JKI7Az8mCan57f7yk71+s5XwPyeeeKLndXoijiKRCPLy8ryoKuOQrT2gi1BZJBpFXiiU8vqp1u/mPTLLjO9IknsEAEIF07vog0cR5SGEENa9RbFJaWUglJJAsuYgxdaJaNOMKBxqJGp6kaTutbGG0dSI5l2yCiXjO6BNVg8Awaj+nhew9a5iFu+RVSAZ4TNnmM3pLeqRMHILp3EOpoQQhiaOmBITRSnlGiVIxLaJp54M/OiyfiQSRV6i2dFz0DuVc8+DJPjJVoJww5MnwJqaGt/0TCBbM4MQAqtr1npjr7M3WtzyJPOtWXuuMW7/IdfXkYEQVrUxCEtOjOkBceTK8IAzQTlo9lqziodAfghKfp7tO9d7swXyA7ZkaKMHWTA/gIDxXhD/4iEOXqDn+xQEXdcx6ggVBs16tIEc9QTsoIJAQVCzJT9ktkXJz7N9TyaMnMfEPFaBoK1ccIbVrUybQgSwH3vnuEZuXqNEgqQ7idhd4Mf7yy/2+s1WgnCDco4ID+liAK5UQmsJErNTyT1yeo8k9LE+OGzJ2RASjDEtR4bBEnIzPEeAjAIsCMiIVm6Mc+T0IElFt0+vn3PNayR5rPeeGo7aPEdqJJa0rfVUc883kqpAQA+1BfICCARjg0s6846s5Ub4zOhZpoSMedICYIo9Cdscx4jzhMLIloDtJiIDwVjvNIb4JGyXIRhiXiIeL5yM89eF16i7ITXbtgRBEC6QOCLSw6NQWVrbuU1Ga+25ZpRJYeu5ZtaD+PAaGAMLBMBUQHJVF0ghsGg4TiABABMxsWMIJMY5RESLewl98EgR0YSQFlbTcpEMcSJVYYbbYmJIQCrMFEXOn+yA3jMuUBhEwKX3ibV3GhATS4YA0sq0EJozCduYL83ohWaMfm0LpVmnBwlYeqiZA0DqCeyBoO6pM85ZgiTsVMY1sjXQA6+RByE4giByl0svvRT7778/Tj31VM/q9EQc+SmpjWzNHDyVBNtMeI8s9Uh9E01MWcSTkZTNFUBEwfXxeCAFWCAEGQ3rU4noAokrYAG7B4lb7hapCDA1Jj5YOGrmIUmuCyWbx0iFQBQBJQSpCghd9HAhzPGNrILJwOzKH+BQAtr+uEUkWT1ExjJDFBmeIqZwbSoQwxOkcFjDaJp3yTL6dTJhpHuO9BMe65Wm91TjTLqH05xJ2MnGNcqK10j15f3lF/xka7ahrvzeoygKNm7c6GmdnoijiRMmeFFNxlEUhWz1AhdvkGbveO1LssEdu7ufVL1HSB5eYwFAAbBbeQGkqgKMQUbD2o88ABmJaAIJujCyCiSVm54dqQrNgxQKmuLG8BwJVRM8jHNT/BieJKmqurCyJJerxkS2McFkEApHtPc8jkAoqDfJLpKYTSzpg1sqjgRsiyjiFs+ROSWI1ZvkTL52EUYsGDSFkfEeUBTsVp5nrp9yOK0XvEa269UH5PTzwIHfbCX8z6mnnooLLrgAZ511Fvr37+9JnZ6Io9bWVhQWFno66VsmkFKira2NbM0ANnu7WjmT3iMDa3jN+gPNAclUtEZUFOmeGNNzpA8EaRNIQokJJcDsxWbkFEkudI9QHtRwxPQiaYM6asLI8CRJ/buweYtUM2/JKpgMFGM+tfyQKY7MQ2aII6PbvF7GLULIKYqYxYOkhGKDO5riiCvxwsjIMbIII2N6EGPcI6YokIyjNSLRN8g1MWo97s5wWiIy7DUySHh/5WhIzU/PA7/ZSvifjz/+GBs3bsTIkSMxZcoUlJaW2pZfcsklCQeITIQn4qh2/XpMGD8+51W4EIJszRCavRswYfw4zWvRHU+RG4YwMhKrhUMwJfMeGesbYx8ZyxjH2qYIdh2QB0Vh5vhHsIXRIrEQm00ohQFFASIRTSQpsVwjw4ukTV0i4kQSgpqXyPAmaWUBs8eMVTBZDoD2FgqBm4M8xoQQEAthOAWRUeYURUZuEXOUm54gYxwjI7fIRRgxPQnbKqQEONY2bsduffpASdQ7rYuu+yYJJqjtKYZN1uvVP/eXP54HfrOV8D/9+vVLmm9UWFiYdp2UkE10j54mZqfjPXKE1+LmXOtKIKlqLLwGaIMIGTlHYLHealHYBBKE0JK0haot198hVG0552DRiM2LZOQiWUUSNzxIIl4oAbEwWkwcxdoW4PogkHkhBELGKNz2cBrjPK6cO7xGbqIokbcoLpRmdtfnCYWRltPF4oWPcc5SDKclnEMtFa+RE0rEJnIQrt+f2djPzsLs2bMxe/ZsT+skcURkBNdRr3u6fQrhNefgkKZ3SQ+vSQBgEuYcYPraToEEoWi5SEa5IZoCAAS3hdmYUKBwBSIaMcNoVpEkuBY6k6oADwIrN9bj6Y++xPurv8NP994F5+27m2arHjWziiNF/8FW8kJQ8uziyDwshgfJkpjdlSgyc4sco1mb+UIuwsj0LFmFkbZjfb8cYLALI6tXyCqMnCQLp6UKdd8niJ0eIQSklD32WnrytMgLhXI+tgwAjDGy1UssPzaMMeTldWGv88fJbd24dVw8Ba6eBeb6g2p6Ihzj5+QHA/ZeVdYxexyJxlbhYBsAMRACC+pjAAWC4KF8KHl55sCKRpd4JRREID8Pgfw8vLt6A+Y8sxCV5f3QFo5g6/ZObQDJUMB8cdtLHw8ppJhl1nUD+SEoQWMQSm1QRyU/ZO5PCQXj7cnLAw/la20NBsGCIXubjHa6CaNAyC6MLGMegQeQFwjE5RklEkMJw2kJzn1auUZdCKG46zXHhZMvngc6frOV2DF45513MHXqVBQUFOCZZ54BALz88st4+OGHu1WfJ56jMWPGeFFNxuGck60ZgnOOMaNH28q67T1KJTm7O+E1Pf9IURSMG1yqbSuipgcIsHiD9CRtFghBClULkUWgCQZLmM3qRYKiaD3auAIIFVKokJb8IqkIHLRLFT7ZYxykKvB/H34JHlCg5Ie0aU2MY2nxHIV0y0J5mgAC7J6jWM81ex6S00vEzORpi6cISOgt0uqIDfDoJhadXfY5VzB+SFnsXHQ3nJYsCbubOLd3u15zGT89D/xma7ZhnJn3bab3s7NQXV2NE088EVdddZWtt9phhx2G3XbbDWeccUZcknZXeHKGGhoafJHYJoQgWzOEZm9j1/am4j3qalu3ruHW+liCH2XdgySkxLa2MFQwbfAiNw+SMTK01YsSDLp7kUL5WsKyvq3hSWKBkDb9iGX+ssK+fczvRmjP6llSgrHPgfw8cH1+Kp6X57qOEgrGvEPm1CAh2z654Q0zPEWGuLHY7vQWmW0w25pEGPEAJA9AgGFba4c2iEKqwihROC2RGPLAawSkcb3mCH56HvjNVsL/PPfcczjvvPPwm9/8BhUVFWZ5YWEhxo8fj/feey/tOj3xHH2/cSMKCwvNGB9jDJxzM/ZnkG455xyMMai23jsxte+8sBOVK4oCKSWi0ahpayAQ8MTGTLVJVVV8v3Ej+vbtC8ZYwjZZyzNte8I2Ma1LrHZs+5jXAeccEgxSn1ne1lYpYrZLo01cb5NeIAUY0wZCFJJBStUshxRQOIdQ1VgPNinAwMDN9bX0Ikjo5RwCEqqQ2LCtFUX5/QAOKDwAVWgrSq0PGjiXYIqCaFirRCoBgClgTAUkoEpovdaYluzNmAJEw1CZ5jWCwgAF4GoUQBBSSNObBEVA0YwCAgpkUE82EgJc4RAAJOwT0bao2thIxlHPYwwFeUG9x5yiebIUYxBMbfJXwQMQZg6SovnUuAKVWUa55prHR3IFAtC8RIomijhn+vocTDEeFRwK10YYV8EBKJCSwfDVbWhoRVFhHrgl117hHCq082HkgDEwcOX/2zv3+Ciqu/9/ZjZXk2yuBBJMQkK4CQIKeEVELuIF77f20XqtttiW+nhpteqjbam0Xmu1l8f6q2294K2Wtv58RCsqImrFPgo/ICQhkASSEBJyB3LZmd8fuzuZ2Z1Ndjczs3vC5/167WuyZ2fO+ZyzZ2a/+Z7vOccFRVGhSIMrm0uyBFl2weNbxBPweRAl1Xe+Yojjl2XJeD95I/AN95N/0Uet7wG6Z8ExcCUkwuVC/NxPJs8I/fMgcPr5cM89p+s0+CxIMzwLrHyWW1WngQHjs4mIyb59+zB79mwAwUOlCQkJOHz4cMR5WmIcHTlyBJWVlZqrMCsrC+MLC9HY1IT29nbtvDF5ecjPz0d9fT26e3q09MKCAmRnZ6Ompga9fX1aeklxMdLT01FZVWW4GSaWlSExMREVO3cadEydMgX9/f3YVVOjpcmyjGlTp6Knpwd79uxBe0cHKisrkZKSgvLycnR0dKChsVE7Pz0tDSUlJWhpacGBlhYt3ek6qYqC9o4O7QYOVafaujotPTkpKTZ1KjoWqamp6OjoQGVVtdY5vXVKQEVlleF7mjZ5Evr7+1Bds0dLc8kypk0uR3fPIdTu3edLVZGclIRJpSVo72xHw/5m+C2p9GNSMaEwHwfau3CgtU1Lz844BseOyUFDaxvauroBAJKqIj8rDWMz01Db0o6uw0fQdqgXOxrbUJSdhpy0JFS3HsaRfo83H0VBaWYiMhKBik4V3p1DZEBVUX4MkJAAVBxO8i4R4HvoTks6hH7Jheq+FHgtAxWyqmCqfBA9iow6V6Z2brLaj4n9zVAkF9oS3diVUQIVQJpyBMX9LTjocqNFzgAAdLm8N/XMH/zK0IbfvOJC/OjSs5CvdqMuIRc9cqr3A0lCgdqFbBzBblce+uDyedMklLgOId2lomrADQUS4JEARUZ5ch+SXLK3TpC086fnJqFPlVHVMQCgF4AMWR7A8QVJ6OoHag52e8+HhOREF8rHZqLXo2D7vjbIPg9RemoyJhSMwYG2TjS3d2v6s93pODY/Fw2t7Wjr8vcxCWNyszE2Lwf1jc3o7jkE1deXxo/NR3Z2NnbtqQvqexnpaaisrvEaVL7zy8tKkZiQgB2VVdAPsk6dMhn9/QOo3rUL7e3tqKyqhishIb7uJ5NnhKooUHxGQVV1taEvDPfcc7pObrcbnZ2dht8Eq5/lVtWp7eBBzJ03D0RsJk+ejI8//hgrVqwwGEd1dXXYsGEDHnnkkYjzlFQLVsHavHkzJk+aFPeeo/7+flRWVWHypElCeI4qq6q0tULi5b/CUHVSPAPYUbETkyeVG/5b9NdJHxukpes9SqqJ5wiABMXrgfJ4fGUOeolcsgxF8aX7ypBUFbIsQVFUqD4PE+CNRJKhwuMZgMczgIq9LZhWkI0EWYLs+z4k//mqAln1AKoKz8CA1+Pj8XjTfd4fRVG9XiDF67mSfN+n4kvb3bAfVzzwFCSoUFXguqWn4TsXLPB5t7z+qVnfWY2LTp2J/7pqma+ugKwMGDxHbYd6UXLjg9jx67vhTk3S0pOTk5GS6PL6VmS/58h3/0GFLLugSL503/CXLLsgu2Svd0sXVyT7PldlFyBLWmyS7BtGU1QYAq9dLhdU+DxHhuBrCf+vvhVTi8bA5UrQhsxcsgxvrQeRJO/wnbeu0PKRZJf3+/B5/FR9uiwFe45cuvtJN5zm72OegKebP937LKjG5MnedY7i7X4y8xz5nweB/xnHo+doR0WF4Tchnj1H7sxMOEFnZycyMzOx66EVyEhJtr28riO9mPij36KjowNut9v28mJJa2srZs6ciYsuugg7d+7ErFmzUFBQgCeeeALz5s3D3/72t4jztMRzlJGerhkbekIFu0WaHmpKXiTpkiQhISEhSKtVGq2ukyRJyEhP1x4qoepklh6LOkmShIwM837gcrkgqcGxRUHaVdVXJ/253iE4yeWCrCrae/9R9u2P5j/Xb+DIsgTABai6YG5V8f5oA8hITYErIcE71OSf9qlKXp3+l+KBKyEBULw//IB3gUZJ8RtJsnfKv+IBXL5hIQ8AlwvF4/Lxwr3f1h7KeRnHIME3fKYqinetJMlrmCUk6m/DBOhbJdH3656Z5UbWMSmm34cL0IydwWn18A5/+Y0gXUyVCzCuW2RY7To4YNsVEHjtf7kMhpGMAVVCxjEpcLkS4HIlGGaXySHijGRZb2ANHl0STGenGfqWLk+Xy2Uaa+QK0YcTEhKC+ms83U+A8f7QPw8ieabEok6KooT8TbDqWW5VnRISuJrNaCA3NxcbNmzAf/7nf+Ljjz/G+vXr4Xa7cc011+Dhhx+OKk9LekZJSYkV2diOLMvUahOyKwElxcUhPx9u3SLve5OFIXXnhVwcUpLhXz07aP0j3ww27XoALlcCSsflaF4i/TYjhpluMgwz2aB4vNtkAF4DQvHFF+mMJMkXO5OUnIzpk8q063xjc96VsxUPAO9ClJIrYXAjV105mgTZNXjUGUDG5pGN6ToDCfrrMIxR5K+XzjAKnJFmCKz2t6886CEqHZdrMH6GDMAOYRgBYSz2GEYQ9lAz3Lz314SQn8cbIj0PRNNKRgcTJ07E3//+d3g8HnR3d8Ptdo9oqQZLjKPm5mbk5eXFfUdTFAUtLS3UagOa3tyckHrDMpCGYbjVs8MxkFRVxYGOHoxxHwNZkgen+Xsz8f6oqopWjiQr3in7PmNI24bEXwXAazwEGknehvEZU16Do7nlIM696xcAgD37W/GHtz/GPz7dgtnlJfg/d17vy3FwDzW131uKmpjsnVmmR2/0mBhI2md+g8iXbjCK/OdGYxT52tyfrkDCgfYe5GW7vdNghzOMdOn6Y8TT9iM0jABAUYGWA2I8twCxngeiaXUa//IaTpRzNOJyuZBpwVCpJcbRgZYWy3bCtRNVVanVJjS9Odkjy2gY75Fpmv+HUFXCMpAUSGhu70GeOw2QfLEwLp/RNZQXyWcAGYwk39pG3plWRk+St3ijoZSbnYnn/+u7xnooCo5J8Rk/ijEmAy5fXJbLN9Ve0+My/9vfNGYGERCZp8jfxkN4iwznqMD+jm7kZmX4jKphDCNDniYP8nC9RlEg7P0lgF7RtJLRwUsvvYQ//vGP2LdvX1Bs2+rVq3HJJZdElB8HXIm1DPMfu6XDayE+H9ZAkuCdBSXJOusneLFI7Qfd70VSFeNQmxxoJHmMw21AkKGUmJCIGZP9w20mG80GGjoJPuPIt6aSGYPGjdF7FGQQ+T/zx9gEGEXea4bwFvnbUA40lmTNmBx8H4ZhZILdw2mD13iGPoeQoxBVVfHVV1+hpaUFM2fORH5+fljXbdu2Dbt378aCBQtMg7+7urqwZcsWpKSk4LjjjkNqamrQOb29vdi6dSs6OztRWlqK0tLSsHW/9dZbuOmmm3DTTTdh+fLlQR7LadOmhZ2XHxpHJD6wMv5oWAMJACTfD7wxe81AAsy9SD5DwDvU5gk2kgBzbxLgNZQAg7EEwOsRCvQY+VX6A/QTvQs4BmEYWjMaSQaDyJcu6QNZhzCKAAw7jKY3jgYNEil8w8iGOCNCSHQcPHgQ559/PmpqalBaWootW7bg5z//OVauXBnymnfeeQc//elPsWfPHuzduxf/+7//q603BAB9fX2444478Oqrr2LSpElob29HS0sLfv/73+OCCy7Qznvvvfdw9dVXIzs7GwUFBdi8eTMWLlyIV199FSkp5hNR9Kxbtw533HEHVq1aNaI20GOJcZSVlTWiwCenkCSJWm3CoHeYOKKRbko7UgNJkmRkZ6RBklxQJTXQPhqMJQrlRfJ/qDOSIA8OtwHQvEkAvIYS4PUoAcHGEqAZTIHIvjgjOSHJu0p10AmDeZgZQwCCDSLf0RCnFMooAkIOowWeL6kqst1pkPwtaqVhFCbheY0Ev7/iHNG0Ol/m4AbRdpcTCXfccQe6urpQXV2NjIwMvP7667jyyitx5plnYtasWabXNDU14Wc/+xlycnJw/PHHB33e29uLKVOmoK6uDsm+1f7/67/+C1//+texd+9ebUuPFStWYNmyZfjTn/4EAKivr8eUKVPw3HPPYcWKFcNqz8zMRE5OTkT1HQ5LvqHxhYVxH3gHeGcmUKs9BOkNY3gtiMC0MB5cQT+qgUc54AdfkiHLEo7Nz4HsGhw6MnhD5ME1eiDLvpWwdT/4csLg+XIC4PJtu6HbgsO/nYi2HYdvSw7/thz+7UUGX4mmL5cvzsgV4nN9Hlq+iYPbhOi3+9C2ONHrdCUa6qvKARvH+mKX1IC2CW43CbJLxrFjcrz7vEVjGA2FZcNpfkmC319xjGhaideIeeWVV3DrrbciI8O7AO3ll1+OsrIybRNXM6699losWLAg5OcZGRn47ne/qxlGAHD11Vejp6cH27dv19K6urowffp07f2xxx6LrKwsdHV1haX/oosuwosvvojOzs6wzg8Hy7YPKRg3Lu47mqIoaGxqolYbiEavFfFHhnzC8SCpChRVQkNLKwpzs33rIfl+pBE0yjboLfJ7kYDQniRV8QZ2G7xJijbs5m0oz6Anx7BWS6Ix9siH4jtH8W0Ca2iCEGvDAAiatRbkJfJrRghPERAytijoGt/5iqKiobUdhXk5wXFQ4RhGIxhOi3SG29Fwf8UK0bSOdgINhuTkZIOxAgBVVVU4fPhwkIdo1qxZ+OqrryzVs3HjRrhcLkyaNElLe/zxx3H33XcjJSUFBQUF+Nvf/oaioiJ885vfDCvPjz/+GLW1tSgrK8PcuXODhuJWrlyJRYsWRaTTEuOovb0d48aOtSIrW1FVlVptwlTvMMNrIbHaQAKgXwdJxQDaug6hIDcLWoyMLrYIMDGSAOOMNm+lDUYS9Bo0o8o/lOYzBgKH1vzojSY9+mGwoT4PeG9w2wfMPPO3l5bmJ9AoCrjG4A0KMIy8eUpo6+rBuDG5voUpnTGMwiLgulFxf8Upoml1Gsnl8npXHSgHAIqKigzpDzzwAB588EFDmn9rmMChqdzcXNTptmoZKbt27cIPfvADrFy5EmPGjNHS586di/Lycjz99NMYP348duzYgZUrV2rDbsORk5ODK6+8MuTnaWlpEWtlQDaxl2EMpGFnnmnvozSQgMG/tbcyvEaRiWEwhBfJnx7KSPJrMBhK/vJd5saS92PFdDo+gMEZaglJoWermRlC3g8Mx5BxPaGMIv9xCG+Rvizvt+ONTzJd4NFMi5meQF3DnBfxukiEHEXU19cbZpAFeo0AICnJ+2w5dOiQIf3QoUPaZyNl7969WLp0Kc444wzDqtV9fX1YsmQJli9fjn/+85+QJEnbSDYxMRF33XXXsHlfc801uOaaayzR6YdPFRJzwv5xCxWDpLve3CMSkGYShxRURmBMjS7WRvvMlWCMSdJdq49N0uJ45ITBfFyJQbFKhpcsay9vlr73JudqsUOuxKBygjTojRt9TJErwdgeujob2iHwe9C1R2D7hfoeojKMQhBevBIfc+Toxe12G15mxpF/2vzevXsN6fX19RFNqQ/Fvn37sHDhQsyYMQOvvvqqYduWyspK1NXV4Rvf+IYWID9+/HgsXrwY69atG3HZ0WKJ52hMXp4wMxOo1R6G1BvG8FrYq2dH6kECgobZJEnFmNxs7yaZkmT0NvnLAKD3IgEwxhb5joaZbYBupW0Ee5T0WgCjRu0a3/W+1W0lV+Lg0aWLORou7sbMINB/N3KArlCeIsNn5p4cbXNYlwtjcrIGvWMmBlLUhtFw9Q1FiHNG1f0VZ4imlQBjxozBiSeeiDfeeAMXXXQRAKCxsRGbNm3Cc889p533xRdfoLe3F6eddlrYefsNo+OOOw6vv/56kCeqoKAAgHfI7ZRTTtHSd+3aFfb6RA899BDeeust089cLhfy8vKwePFi3HzzzUg0WxLFBEuMo3AXioo1sixTq00MqzdWBpI+3XeUZRfG5uUMnus/TRMShpEUUKY2nObSlRtoKPnP19XXUF7A5wC8e6/5jqoc4nYdykgI1yDSHSM1ivz5ypLsbVezvGGtYRQWQ1w36u6vOEI0rU4Tr9uHPPzwwzjnnHOQm5uLmTNn4le/+hVOPPFEfO1rX9POWb16NZqamrBx40YAwO7du7Ft2zYtLumjjz7C3r17MX36dJSWlqKrqwuLFy9Gb28vrr/+erzzzjtaXnPnzsW4ceOQm5uLm266Cd///vfR1NSEY489Fn/729+wZcsW/O53vwtL+/HHH4+nnnoKSUlJWL58OXJyclBXV4c33ngD06dPx5gxY3D//ffjww8/xCuvvBJWnpYYR7W1tSgqKhJiZkJ9fT212oCteiM1kADNYDEzkDyKgvqGJhQV5MMlIWg2GwKNlnCMJB2mhhJgNJYAU4MpEI8qDR6HMxICDQvZxDAZYrgxXKPIcK4u6NqjKKhvPICiwrHedh1uuHM4/UOcP9I4I95f9iGaVuJl8eLF2LRpE37/+9/jH//4By6//HKsXLnSMAQ2d+5ctLW1ae+3bt2KZ555BgBw/vnna8Ngt9xyC0pLS9Hd3Y3y8nIAwB/+8AdDeffccw/GjRsHAPj973+PJUuWYP369fjss89QVlaGbdu2adcOh6IomDhxItavX2/wTP3kJz/B/PnzsXbtWtx3332YMWMGtm3bZlg2IBSWGEfdPT1C7FGjqiq12kRYeqP1HoW6NpSBpDtfG/IxDGEp6D50ePA8QBesDeP5gUHhupODjCQTjao+zaXTomeoB7SkO4YaAgj4AQoyHIYwiAznhzKKdJ8NuQ2IJKPbH9AZSXzRMGUGYkWc0ai8v+IE0bSSQebNm4d58+aF/Pzuu+82vL/wwgtx4YUXhjy/oKAAb7755rDlSpKEr33tawYvVSR89NFHuPLKK4OG7EpKSjB37lxs3rwZy5cvx4IFC1BRUeGccURI2MTAQArOMyC+JnBNJAwx1OYvU5eP3gAyNZQCdKuB9dC5v4PqLeuMETNPkFmdQ70fzpMTiVGkv9bgadOtGxWnhhEhZHShqio2b94clH7kyBFs3bpVe9/Z2YnCwsKw8qRxRJwnLgwkKfgc/Y+8bqjNcLapkQQEepP8+QYN6w1VDwT/+PvjjFR5iJgjfZ4h3of0Jg0zA9BwXQhvke4E8/JoGBFCbOS6667DSSedhP7+flx66aVazNFvf/tbqKqKxYsXY/v27ejq6hrSM6bHkidJYUGBEFH/kiRRq01ErDeMH7GwvSNeAUOXpf+xl10oHJsPSQpYLTrwb523JmiLkSBjwzc1Xr9PmTQ4DT5oOr0kG6f2h3hJ2qKOrtDnmeSjTeE30y0HLD0Q2E766wDjukVDtJckSSgcN9Z00Unz7yV2htGov79iiGhaifjMnDkTGzZsQGtrK66//nosWbIEd9xxB44//nhs2LABqampyM/Px/r16w0xVENhiecoOzvbimxsR5ZlarWJqPQ66UHSXSPLErKzs4xeHSDYe6QZB77rlRAxTGY6NAI8QSF0hdqIV/YZGrJ+2w99fmEPrw1jPJrlN5ynKKAMyeVCdlameflBZcbWY3RU3F8xQjStZHRw0kknabPhenp6glbFzsvLiyg/S3pGdXW1EFH/iqJQq03YqXdIAyASI8B3jaICVbtr4VGHGP4J/FvvSZLl0F6ZoPIk4yuEB8g/bGbwNEkyBnzW1ICKIC9UkCfKzDNk5iHS1ymgPH0dg+oU4m//tYqioGp3HZThYlwdnJUWCt5f9iGaVqfxT+V34nW0Es12IYFY4jnq7esTIupfVVVqtYmo9YbhPQKG8CCZ5eH/8Q2hRVWB3r5+7eOQ3iD9D7NZTBJg8CYBCJ7eb+r1GsqL4zLq1lac1k3lj2YoIMDICDI6zAKtTa4bKo5JhezrA6E0RLaGUfgrp0f+I3DU3F8xQDStREweeeQRrFu3Dj/4wQ/w1VdfDbma9g9+8AOcffbZEeXPgGwSe+wwkIDwhtl01w05ZBZq6E1vVAQaSkOtgD0Uhu059MZRBEZROENwgUMKYRpFQXlpfw+1JEH8GEaEEPGZMGEC5s6di9zcXO3vUOTm5kacP40jEh/YaSABwxtJQPRGkv994HpDZk6j0CqMDFXHcC43O88svmIYI2hYj1M0sUXDXEfDiBAyHFdccQWuuOIKAMCcOXO0v63CEuOopLhYiMA2WZap1SYs0RuBgQQg/EBtwOBFkmUJJceOhyybzNYKXI8ICPYADffenxbYFgGeJTMCg8RDBWSHZUCEYwyZpQ1nEIXIJ6hdIzSMIoovGqFhdFTeXw4hmlan0W8obXc5o51Vq1bhwIEDOOuss3DmmWdaOhHAEuMoPT3dimxsR5IkarUJy/SGaSABw8xkA0J6kSQAGekhAvZMrg0yxkJ5k0Kl+dOHelgpRq+Vhn9avOwK3xukJ5QREYbBE65RpH0kSd52tdNbNEw+YWdxtN5fDiCaViIu48aNw5o1a/CrX/0Ksixj9uzZWLRoERYtWoQzzjhjRP3QEtNyR0UFPB6PFVnZisfjoVabsFRvBD9+Q/6ohvjMoyjYUVkNj2eoGBnZ1FgIirUxm9EVTnrg5/pZYrqXvzU9oc4JN/9w0kPVM0R7BOLx+NvVpA/EkWEEHOX3l82IppWIyze/+U1s27YN+/fvx0svvYR58+bhH//4B8477zxkZ2fjtNNOw7333ovdu3dHnLclniMRpmz6oVb7sFRvKO+PCcPGIZnk41GU8AKATLxCQUHXgefpyzP7MQ9cKTuc8sMwTsLKM5IhrYiMFgmQfO0aQR6xMIz8HNX3l82IpNVpnJpmfzRN5c/Pz8dVV12Fq666CgDQ2NiId955B48++igeeughTJo0CaWlpRHlyYBsEt9YEYc0VD7hBGzr8wBMh9yCyg5lLJl9NiTy4DEa4yAaj02kRpGVZY9UDyHkqGRgYABffPEFPvjgA7z//vvYuHEj0tLScPnll2P27NkR50fjiMQ/VsQh+fMBAJgN+0RhJAEhDSVgGGNJT5h1C0vPEEQzBBn6/PC2a4lYh1lehBBiQkVFBd588028//77+Oijj5Ceno4FCxbg4osvxhNPPIFp06ZFnbclxtHEsjJhZiZQqz3YrjdCAwkI7UWSXQkonxhCayRGkl+XVrCxPDMjYMgAchOG2z4kFLZt0jqEUTRku4aryVCWfX2f95d9iKaViMvPf/5zrFmzBjfccAM+++yzERlDgVhiHCUmJlqRjSNQq33YrjcCAwkY2ouUmODfekMa+XCbXp9BQHC+4RgIIT1fEeRhnvEIfgjCGT5TVW+7mhBPhpEf3l/2IZJWp5FkyZmYo8ClSkYhV1xxBbq6uvD666/j5ZdfxhlnnIGFCxdi4cKFOOGEE0Zk/FryDVXs3ClEAJ6iKNRqE47pjSQwGeYzrxRFwY7KqkGtQ+U51P5k4WoNNVNsGM2qJMOjesv1qJL5LDILyw3OZ5i6B+Qb1K4wb/+wtNsM7y/7EE0rEZfzzz8ff/nLX3DgwAF8+OGHWLx4MT766CMsXboUOTk5uOCCC/DYY4+hoaEh4rzpUyRiEuEPaERGRcjPozSSQpUT1itgb7VwXiPWN0w9IzDyIiuXjyNCSORIkoRZs2bhtttuw9q1a9HS0oJnn30We/bswZ133ol33nkn4jwZkE3EJYphNi/DrG0y3DICesNhtGxcGY7RF0HgNw0jQszhCtn2UFdXh/fff1+brVZbW4uUlBQsWrQIxx13XMT50TgiYjOcIWOC94c7QmMgHEMJEMdYCtcDFnEQeISeNRpFhJAoef/99/Hiiy/i/fffR01NDZKSknDyySfjuuuuw1lnnYVTTz0VycnJUeVtiXE0dcoUIaL+ZVmmVpuIud4IvEherZMhyTJUSRo2AFrLHxi+jDCMpU8/+xfe+ed7aG9vx/Tpx+Hqr12FlJSUEFolwzFqIh0OjGJmnCyrmDplcvh9IIaGUcz7a4SIpFc0rURcXnrpJWzbtg1XXXUVFi1ahNNPPx2pqamW5G2JcdTf3x+1deY01GofMdcbgRepv38AyclJ3tOHW0DSrIwwywk0Sm793vexo2InFp+1EBPLyvDsH57DL3/1NDa89y6ys7OGzy/C8iK7duRxXPp2taocu4h5f40QkfSKpJWIyzPPPGPb/niWPKV21dQIEfWvKAq12kRc6R3mxzeUVv0ssbDLiTAQ+o7bvo/3330b9/3obnzn1m/jnbfeREtrC5778/PG2WG+l+LzPCmqavp50CsSotA/VBuF1QfixDCKq/4aBiLpFU2r00iyy7HXaMfOjYMZc0RGJ1HEIumJyJsUWKaWSfC1EyeWGd5nZGQgf0w+WlpaItYYMSMwTKJeW8mCsgkhxGksMY5UVTXsbixJEmRZhqIoUHUxF5Gmy7IMSZKCdk72jxMHWv2h0l0ul6bRf7RKo1118mv1v0LVSZ8eyzoBwf0g2u/JljpB1dLD6Qf+72lA0eWhKtbUSadlw0cbsbOyEr9Y/TMoihKkxePxHru6uiBJkpaenJyMlJQU87rKrhB1UiO6nyRXgi598JpQ3xNg8iwIoSXWzwh9HxiqTvHyjNA/D8Kta6zqBJg/C6x8lltVp0A9hPixxDjq7e1FZWWlNnUwKysL4wsL0djUhPb2du28MXl5yM/PR319Pbp7erT0woICZGdno6amBr19fVp6SXEx0tPTUVllXFhuYlkZEhMTUbFzp0HH1ClT0N/fj101NVqaLMuYNnUqenp6sGfPHnR0dqKyshIpKSkoLy9HR0cHGhobtfPT09JQUlKClpYWHND9N+90nVRFQUdnJxRFwcDAQMg61dbVaenJSUkxq1Nqaio6OjoM/SDa78nWOu2tQ1dXt1drVTXGFxYiOzsLNbt3o7dXX6ci3/dUbfI9JaCisspQp2mTJ6F/YADVNbu1NJcsY9qUyeju6UFt/V5DnSZNLMP/27Ed11x/I84771wcW1yCun2NmFBchJaDB9Hsq1NXVxcAYPL0mYbybr75m7j/Rz9C/pg81O3bZ/iexheMQ3ZWFnbt3mP8noqORUZ6Oiqrd8Gjq1N5WSkSExKwo7IK+tlmU6dMRn+/Wd+b4vue6gfrlJyE0gkT0D8wgMqqaq0PxMv9NFgnb9+rrq7WngWuhIS4u58C66QqClR4jYWq6mrTOsXLM8LtdqOrq8vwLLD6WW5VndoOHsTcefPgKLLL+3KiHBI1kqo3qaPkUE9PXP1XGC//QbFOcVwn35CXFXUy8yg1NjXhgR//xPuftAosO3spLr3kYq3MhsZGLF12Lo47bhpe/POfkJiYaKqls7MTBUUl2LVzB9LS0sLzHEVYJ6OHaITfkwr2PdZJqDqlpafDCTo7O5GZmYnGP/4Y7mPMZ6daWt6hIyi4/gF0dHTA7XbbXt5owxLP0aFDh5CWlhYUHBVqmmSk6S6XuQUcSbr/hujp6TFotUqj1XVSVdWgNVSdzNJjUSdVVXH48GHTfhDp92R3nbxt69MKdcjzw9M++LcsuyCpCjLS03HmggVa+sSJZdo1+xoasOy88zFt2lSseeF5JCUZZ3fptfj/Tk9PR2ZmZsR1NU1PMN/3akTfk+Rt10OHemx9Flj1jDB7FsTT/QQYteufB/F2PwXi7QfmvwlWPcutqpMFvgEySrEkSrK2ri7Iwo9HFEWhVpsQSa9Bqw17eamSDHdWNr7xjW9orxNOnAMAaGhsxLLzzsfUKVPw8osvBBlGZlr1x0h1mL0sRdd+wvYBARBJr2haCTGDs9UIAUY8uy0cVEnGDTfdjN279+DEE07Erd/7vvbZvHlzccvNN3ulDKPBcgMnGuJBAyEiIsvelxPlkKihcUSInkgXeYyQ7373O7j6P/4jKH3ChJLBYnUa/H/b4vWJlFiXTwghDmGJcZSclGTrYkxWIUkStdqESHrD1mqDobT8/PMjOl8fDxMTIjCIRmUfiBNE0iuaVkLMsGS22pHDh63QQogY2Dj0FkhnZyfGFhRif2ODczNO6CEiRxEpFu3FNRz+2WpNLz7k2Gy1cVf/iLPVosSSp2BbW5sQgW2KolCrTYikd8Rao9h2I1pGEpAdNhbV56jqAw4jkl7RtBJihiVP9obGRiGmRKqqSq02IZJey7XaaCz5NVrarjbpPar7gM2IpFc0rYSYwYBsQqwmlMHh4HDckDoIIYQMCY0jQpyCm7cSQogQWPK0TTdZCTUekSSJWm1CJL1CafXtjyQJsE+SUO0qkFZALL2iaSXEDEs8RyUlJcOfFAfIskytNiGSXtG06o/xjGjtKopWQCy9omklxAxLekZzc7MQUf+KolCrTYikVzSt+mM8I1q7iqIVEEuvaFodR3Y59yJRY4lxdKClRYiof1VVqdUmRNIrmlb9MZ4RrV1F0QqIpVc0rYSYQZ8iIYQQQogOGkeEEEIIITosCcjOysoSIupfkiRqtQmR9IqmVX+MZ0RrV1G0AmLpFU2r48iyM/FADDYfEZYYR+MLC63IxnZkWaZWmxBJr2ha9cd4RrR2FUUrIJZe0bQSYoYlPWNfQ4MwMxOo1R5E0iuaVv0xnhGtXUXRCoilVzStZJB//OMfWL58OU455RR85zvfwf79+0d8zZEjR/Dwww/jnHPOwemnn4577rkHnZ2dQfkcPHgQ9957LxYsWIALL7wQ69ats6xe0WCJcdTe3i5E1L+qqtRqEyLpFU2r/hjPiNauomgFxNIrmlankWTZsVck/OUvf8Gll16KRYsWYdWqVdi5cycWLFiAw4cPR32Nqqq4+OKL8dxzz+HWW2/FqlWr8OWXX2LZsmXweDxaPvv378e8efPw+eef47777sNtt92Gp556Ctu3b4+ukS2A24cQQgghRzn33XcfvvWtb+H2228HAMydOxfjxo3D888/j1tuuSWqa7Zv345169bho48+wvz58wEA8+bNQ25uLtauXYvLLrsMAPDDH/4QiYmJePPNN5GUlAQAWLRoEfr7++2udkg44EoIIYQcxTQ0NKCiogLnnXeelpaVlYX58+fjvffei/qatrY2AEB+fr52Tnp6OtLS0vDuu+8CAPr7+/Hqq6/ixhtv1AwjP4mJidZUMAosMY7G5OUJMzOBWu1BJL2iadUf4xnR2lUUrYBYekXTOtrp7Ow0vHp7e4POqa+vBwAUFBQY0gsLC7XPorlm1qxZyMnJwZNPPqnFd/3xj39EW1sb6urqAAC1tbU4fPgwiouLcfPNN+PUU0/FlVdeqRlPscIS4yg/P1+IqH9ZlqnVJkTSK5pW/TGeEa1dRdEKiKVXNK2OIzm0dYjkXS6gqKgImZmZ2mv16tVBkvzDV8nJyYb05OTkkENb4VyTkZGB1157DW+99RbGjRuHCRMm4Nlnn8WCBQu0mCO/sfa9730Pxx9/PB577DHMnj0b55xzDt54441oW3nEWBJzVFtbi6Kiori/GRRFQX19PbXagEh6RdOqP8YzorWrKFoBsfSKpnW0U19fD7fbrb0PNGYAIDc3FwDQ2tpqSG9tbdU+i/aaRYsWoaamBnv37sXAwABKS0txwgknYOLEiYZ8rrrqKqxcuRIAcNppp+Hf//43fvOb3+DSSy+NqL5WYUnP7e7pEWZmArXag0h6RdOqP8YzorWrKFoBsfSKpnW043a7DS8z42jSpElwu93417/+paWpqop//etfmDNnjmm+kVwjSRKKiopQWlqK2tpabNmyBcuWLQMAjBs3Dscee6whLgnwjkiZTfl3ivg26wkhhJDRhBNDav5XmCQkJOCGG27A008/jaamJgDAb3/7WzQ3N+P666/Xzrvrrrtwww03RHTNn/70J23to/b2dtx000048cQTtZlqALBixQq88MILaG5uBgDs2bMHb7zxhmZAxQJO5SeEEEKOclavXo36+npMmDABeXl56OnpwfPPP49JkyZp5+zevVszhMK9pqioCKeccgqSkpKwb98+LF68GGvWrEFCwqD58cMf/hC1tbWYOHEiCgoKUF9fj6uvvhr333+/M5U3QVIt8Cs2NjQgMzNTiPHljo4OarUBkfSKpLW9vR0FhYVobGhAVlZWrOUMiUjtKpJWQCy9omk9Ji3NkbI6OzuRmZmJ/W88BXdaqv3l9RzG2Eu/h46ODkPM0XA0NzejtbUVZWVlQUNwe/bswcDAAMrLy8O+BvC2865du5Cbm4ucnJyQZbe1tWH//v0oLi7GMcccE7ZmO7DEODoyxAqahJDo6ezsxNhx47C/qSmiBxwhJDxSUu03VABxjCPixRKzvrq6Woiof0VRqNUmRNIrmlb9MZ4RrV1F0QqIpVc0rU4Tr9uHECOWtF5vX58QUf+qqlKrTYikVzSt+mM8I1q7iqIVEEuvaFoJMYOmJSGEEEKIDhpHhBBCCCE6LJnKX1JcHPezEgDvUvHUag8i6RVNq/4Yz4jWrqJoBcTSK5pW5wuNbA2iEZVDosYS4yg9Pd2KbGxHkiRqtQmR9IqmVX+MZ0RrV1G0AmLpFU0rIWZYYjbvqKjQNpGLZzweD7XahEh6Y621t7cX69evx5/+9CesX78eAwMDIc/1a2S7WotIWgGx9IqmlRAzLPEciTBl0w+12odIemOldcOGDfjeypUoKS5GQUEBPvn0U3g8Hrz1f/8vSkpKYqLJStgH7EMkvSJpdRxZdmhYLf6HNeMZbh9CiIOkpaXhvX/+E3l5eQCAvr4+nHTyyXj88cfx5JNPxlgdIYQQgMYRIY4SuFt1UlIS3G43/9MmhJA4whLjqKy0FKqqauO3kiRBlmUoimJYZCvSdFmWIUlS0Liwf4ZB4A9KqHSXywVVVaGqKkonTICqqlAUxRKNdtXJr1WSJE2vWZ306XZrH6pOsixrbeuvW7TfkxN1Gq4fWN33AtOfeeYZHOntxccbNyLB5cJdd91lqsV/7Onp0foCACQnJyMlJSWm95PZ92TXs8DqOun7gMfjibv7KbBOqqqirLQ0orrGsk5mzwK7+95ItROixxLjqKOjA62trYAv8j8rKwvjCwvR2NSE9vZ27bwxeXnIz89HfX09unt6tPTCggJkZ2ejpqYGvX19WnpJcTHS09NRWVVluBkmlpUhMTERFTt3GnRMnTIF/f392FVTo6XJsoxpU6eip6cHtbW1UFUVkiQhOTkZ5eXl6OjoQENjo3Z+eloaSkpK0NLSggMtLVq643XyGXNTp07FwMBA6DrV1WnpyUlJMatTWloa9uzZ433Y+PpB1N+T3XXq7tb6QWFhoTN9T1enxIQE7KysRFtbG7Zs3YqioiLU7N4NVVWD6tTd1QUAmDR5sqG8m2++Gffde29s76eA72nixIk4dOiQd9duXx+Im/spsE67dml9QHa54u5+CqqTqqK0tBSKomBnZeWIvie765SVlYW9+/ahv69P6wd2972o69TWhjlz54KQQCzZeHbz5s2YPGkSXC5vkFms/ysM9d9Gf38/KquqMHnSJCQkJMTNf4Vm2j0eDyqrqjB1yhS4XK64+q/QrE6KomBHRYWhH8TTf4X69IGBgWH7wUj7Xnt7O15+5RXIkgQVwOxZs3DyyScHaenr68O5556LnJwcvPbaa0Fa2traUFRcjJ0VFXC73XHtOVJVNagPxMv9FJiufxa4XK64u58C66R/HgROP4/1/RSYbtYP4tVzNDAwAHdmJpzAv/Fs85vPwJ1m/47znT2HkL/8Fm48GyWWeI4kSdIeMHr8HTyQSNMD840m3a/Rf/SXZZVGO+okSZL2GqpOdmmMND1UP4jme7JLoyzLEfWDaPvewMAAqqqqtPTioiLT+yMlJQXLli3Df//3f5tq8V+TkZGBrKyskHWKJN3K+0mPx+Ox/VlgZZ0Ctcbb/RSoZahngdn5/mucrtNQ/cCuvhepRn96qHIJYUA2ITYwduxY/PKJJ4LSq6urUV5ebkj7eNMmlE2c6JQ0QkgMkVwuSA4YZU6UMZqhcUSIgzz66KNoamrCSSedBFmW8e4//4nKykr89Y03Yi2NEEKID0tijnq6u7Ux5XhGPzuJWq1FJL2x1rpx40Zs2LABfX19KC8vxyWXXIK0tDTTczs6OjCuoABNjY3IdCg2Ilpi3a6RIJJWQCy9omlNPcb++B9gMObowP/8H8dijsacexNjjqLEEs9Rf38/kpOTrcjKdqjVPkTSG0ut8+fPx/z582NStt2wD9iHSHpF0kqIGZasL76rpiZoVkE8oigKtdqESHpF06o/xjOitasoWgGx9Iqm1XFk2bkXiRq2HiGEEEKIDhpHhBBCCCE6LIk5CrWORDxCrfYhkl6RtIqESO0qklZALL0iaXUc2eV9OVEOiRpLZqsdOXzYCi2EkAA6Ozsxdtw47G9q4owTQmwgJTXVkXK02Wrv/tm52WpLr+VstSixxLz371UV76iqSq02IZJe0bTqj/GMaO0qilZALL2iaSXEDEuMo9q6OmFmJlCrPYikVzSt+mM8I1q7iqIVEEuvaFoJMYMrZBNCCCEOIckuSA7EAzlRxmiGUXOEEEIIITosMY6Sk5Lifpl4wLubM7Xag0h6RdOqP8YzorWrKFoBsfSKppUQMzhbjZA4hrPVCLEXp2ertaxfA3e6A7PVug8hb9HXOVstSizxHLW1tQkR2KYoCrXahEh6RdOqP8YzorWrKFoBsfSKppUQMywxjhoaG4WYEqmqKrXahEh6RdOqP8YzorWrKFoBsfSKppUQMxiQTQghhBCig1P5CSGEEIfgVH4xsMRzlJ6WJkTUvyRJ1GoTIukVTav+GM+I1q6iaAXE0iuaVkLM4Gw1QuIYzlYjxF6cnq3W+sGrjs1Wy114JWerRYklnqPm5mYhov4VRaFWmxBJr2ha9cd4RrR2FUUrIJZe0bQ6jiwDssuBF0OKR4IlrXegpUWIqH9VVanVJkTSK5pW/TGeEa1dRdEKiKVXNK2EmEHTkhBCCCFEB40jQgghhBAdlkzlz8rKEiLqX5IkarUJkfSKplV/jGdEa1dRtAJi6RVNq+PIsjPxQIw5GhGWGEfjCwutyMZ2ZFmmVpsQSa9oWvXHeEa0dhVFKyCWXtG0EmKGJT1jX0ODMDMTqNUeRNIrmlb9MZ4RrV1F0QqIpVc0rYSYYYlx1N7eLkTUv6qq1GoTIukVTav+GM+I1q6iaAXE0iuaVqeRXC7HXiR66FMkhBBCCNFB44gQQgghUFUVmzdvxttvv43GxkZLr+ns7MT69evx73//e8jhzH379mHt2rWoqKiIWL+VWGIcjcnLE2ZmArXag0h6RdOqP8YzorWrKFoBsfSKppV4aW1txUknnYQLL7wQq1atwsSJE/H4449bcs0vf/lLFBYW4r777sNtt92Gs846CwcPHgw6r6+vDxdeeCGuuOIKvPzyy5bVLRosma2Wn59vRTa2I8sytdqESHpF06o/xjOitasoWgGx9IqmlXi5/fbb0dvbi6qqKqSlpeGvf/0rLrvsMpx11lk44YQTor7m5Zdfxl133YW3334bixcvBgB8+umn6OnpQU5OjiG/u+66C3PmzEFra6u9lQ0DS3pGbW2tEFH/iqJQq02IpFc0rfpjPCNau4qiFRBLr2haCdDb24vXXnsNK1asQFpaGgDgkksuwcSJE/HCCy+M6Jqf/vSn+I//+A/NMAKAU045BUVFRYb83nzzTbz99tt44oknrK5eVFhiHHX39AgzM4Fa7UEkvaJp1R/jGdHaVRStgFh6RdM62uns7DS8ent7g86prKzE4cOHMWvWLEP6rFmzsGXLFtN8w7nmwIED2L59O84991zU1dVh3bp12L59e1Be+/btw80334wXXnhBM7RiDX2KhMSQzz//HFu3bo21DEKIU8gu514AioqKkJmZqb1Wr14dJKmjowMAkJ2dbUjPzc1Fe3u7aTXCuaa5uRmA1yt0xhln4LHHHsPChQsxf/58LeZIURRcffXV+N73vod58+ZF16Y2QOOIkBjx9K9/jTMXLsT1N9wQaymEkFFKfX09Ojo6tNc999wTdE5SUhIA4NChQ4b07u5uJCcnm+YbzjX+c3bu3ImKigq88847qKqqQmNjI+69914AwLPPPouKigpMnToVa9euxdq1a3Ho0CFUVFTgzTffHEHNR4YlAdmFBQVCRP1LkkStNiGS3njQ+uWXX+LJJ5/E17/+dXz55ZchzxNttlqs2zVcRNIKiKVXNK2jHbfbDbfbPeQ5ZWVlALyG1Jw5c7T0+vp6lJaWRn1NcXExEhIScPHFFyM1NRUAkJmZiXPPPRebNm0C4PU8nXLKKfjzn/+s5dHd3Y0vv/wSkiRh+fLlkVbZEizxHGVnZwsR9S/LMrXahEh6Y621u7sb1153HX715JMYM2bMkOeKNluNfcAeRNIrmlYC5OXlYe7cufjLX/6ipe3btw+bNm3Cueeeq6V9/vnn+Oijj8K+Jjk5GUuWLEFVVZWhvOrqaowfPx4AcMUVV2geI/8rPz8fX/va17BmzRrb6jwclniOqqurUVZWFvcdTVEU1NTUUKsNiKQ31lq/f9ttWHTWWTj33HPx4YYNQ54r2mw19gF7EEmvaFodRxcPZHs5EfDII4/g7LPPRnZ2NmbOnImnnnoK8+bNw1VXXaWd84tf/AJNTU3YuHFj2Nf8/Oc/x4IFC5Cbm4s5c+bggw8+wAcffIAPP/zQmnrahCXG0ZHeXgwMDMDl28tFkiTIsgxFUQyzASJNl2UZkiTB4/EYyvPfcIEdO1S6y+WCqqoYGBjQtCYkJFii0a46eTweHOnthaIokCQpZJ306XZrH6pOqqoG9YNovye76xROP7C67/nT16xZg39/8QU2bdrkLdNXrsfjMdU+MDAAwDvjBBicXZOcnIyUlJSY3k+B35NZH4iX+ykwXd8HXC5X3N1PgXXSPw8CZ1jF+n4KTA/1LLCz743kWUC8LFy4EJ9++imeffZZvPvuu7j66qvx3e9+V/sOAeCkk04yBGiHc82sWbOwefNm/O53v8Pf//53lJaWYtu2bZg4cWJILWeffTamTp1qSz3DRVItmMu4ceNGpCQnQ/J16KysLIwvLMS+hgZDQ47Jy0N+fj5qa2vR3dOjpRcWFCA7OxvV1dXo7evT0kuKi5Geno4dFRWGm2FiWRkSExNRsXOnQcfUKVPQ39+PXTU1Wposy5g2dSq6u7uxZ88etHd0ICszEykpKSgvL0dbWxsadEuep6eloaSkBM3NzTjQ0qKlO10nVVHQ3tGBk+bNg6IoIetUW1enpScnJcWsTqmpqfj0s8+Q6XZr/SDa78nuOnV1dWn9YPz48bb0Pf/CaBMmTMDhQ4fgURQkJyfjoosuwu3/+Z9YsnQpujo78evf/AZbt27FqlWrMGP6dMyYMcNQp67OTpy1aBECufnmm3HfvffG9H4K/J5KS0vx1ZYtSEpM1PpAvNxPgXWqrq7W+oArISHu7qfAOqmKAkVVMXXKFFRVV4/oe7K7Tm63G5/9619wZ2Ro/cDuvhdtndoOHsRch2ZIdXZ2IjMzEwc//x+40+2frt7Z3YOceeeio6Nj2JgjEowlxtHmzZsxedKkuPcc9ff3o7KqCpMnTRLCc1RZVYWpU6bA5XLFzX+FoeqkKAp2VFQY+kGs/ysc6r/F4frBSPteXV0drrvuOsAX8Pn1r38d5yxbZkgDBmeSzJg+HQ8//DBOOeUUg5a2tjYUFRdjZ0UF3G533HuOAvtAvNxPgen6Z4EoniP/8yAwiDjW95OZ58jsWRCvniN3ZiacwG8ctX2xzjHjKHvOMhpHUWKJcdRy4ADS0tLiPvJfVVX09PRQqw2IpDeetN59zz1499138cXmzaafd3R0YFxBAZoaG5Hp0EM8WuKpXYdDJK2AWHpF05p6zDGOlEXjSCwsiTlKT0+3IhvbkSSJWm1CJL2iadUf4xnR2lUUrYBYekXTSogZlkwl2FFREeQujUc8Hg+12oRIeuNJa3FxMY4//viQn/s1xoPW4Yindh0OkbQCYukVTSshZljiOYrJdMgooVb7EElvvGi9dcUK3LpiRaxlWEa8tGs4iKQVEEuvSFodR3JoKr/kQBmjmPhehIIQQgghxGFoHBFCCCGE6LDEOJoowEqogHd6KLXag0h6RdOqP8YzorWrKFoBsfSKppUQMyyJOUpMTLQiG0egVvsQSa9IWkVCpHYVSSsgll6RtDqOJAGSA0YZZ+KNCEu+oYqdO4UIwFMUhVptQiS9omnVH+MZ0dpVFK2AWHpF00qIGfQpEkIIIYTosGRYjRBCCCFhIMkODavR9zES2HqEEEIIITos2Vutp7tb21gwnvFvWEit1iOSXpG0ira3mijtKpJWQCy9oml1fG+1L9+HO8P+7VU6u7qRPfss7q0WJZZ4jvr7+63IxhGo1T5E0iuSVpEQqV1F0gqIpVckrYSYYYlxtKumRoiof0VRqNUmRNIrmlb9MZ4RrV1F0QqIpVc0rU6jSrJjLxI9bD1CCCGEEB00jgghhBBCdFgylV+kJdip1T5E0iuSVpEQqV1F0gqIpVckrY7DqfxCYMlstSOHD1uhhRASQGdnJ8aOG4f9TU2ccUKIDaSkpjpSjn+22sEtHzk2Wy1n5hmcrRYllpiW3d3dsMDGsh1VVanVJkTSK5pW/TGeEa1dRdEKiKVXNK2EmGGJcVRbVyfMzARqtQeR9IqmVX+MZ0RrV1G0AmLpFU0rIWZwUJIQQgghRAeNI0IIIYQQHZYYR8lJSXG/TDwASJJErTYhkl7RtOqP8Yxo7SqKVkAsvaJpJcQMzlYjJI7hbDVC7MXx2WpbNzo3W+34+ZytFiWWeI7a2tqECGxTFIVabUIkvaJp1R/jGdHaVRStgFh6RdNKiBmWGEcNjY1CTIlUVZVabUIkvaJp1R/jGdHaVRStgFh6RdNKiBkMyCaEEEII0WHJ9iGEEEIICQNZ9r6cKIdEjSWtl56WJkTUvyRJ1GoTIukVTav+GM+I1q6iaAXE0iuaVkLM4Gw1QuIYzlYjxF4cn622bZNzs9Wmn8bZalFiieeoublZiKh/RVGo1SZE0iuaVv0xnhGtXUXRCoilVzStTqNKsmMvEj2WtN6BlhYhov5VVaVWmxBJr2ha9cd4RrR2FUUrIJZe0bQSYgZNS0IIIYQQHTSOCCGEEEJ0WDKVPysrS4iof0mSqNUmRNIbS62qqsLj8QSlJySY34qizVZjH7AHkfSKptX5QmXvy4lySNRY0nrjCwshC7CmgizL1GoTIumNpda/rl2LDLcbWdnZhtf+/ftNz/drZLtai0haAbH0iqaVEDMs6Rn7GhqEmZlArfYgkt5Ya83MzER3V5fhNXbsWNNzRZutxj5gDyLpFU0rIWZYYhy1t7cLEfWvqiq12oRIekXTqj/GM6K1qyhaAbH0iqbVcfzDak68SNSw9QhxmK6uLuSPHYu8MWNw5sKFeO+992ItiRBCiA5LArIDg0wlSYIsy1AUxWCZR5ouyzIkSQoKYPWPEwe6REOlu1wuTaP/aJVGu+rk1+p/haqTPj2WdQKC+0G035PddQqnH1jd9/zpx6Sm4vHHHsNll10Gj8eDX//mN7jwoouw7u23cdpppwVp8Zff1dUFSZK09OTkZKSkpMT0fgr8ngD7ngVW10nfB4aqU7w8I/TPg3DrGqs6AebPAjv73kieBYSYYcn2IYSQYAYGBrS/ZVkOGfy5YMECjB07Fq+99lrQZ/4tBwJ54IEH8OCDD1qmlRBiL/57ubVis2Pbh+ROncvtQ6LEEs8RIcTIzp07MX36dO39D3/4Q/zsZz8zPXfGjBn45JNPTD/LyMhAc3MzkpKSDNOOk5OTrRVMCHEGTuUXAhpHhNjAlClTDJ6jofjqq68wfvx4088kScKYMWOslEYIIWQYaFoS4iC33HIL1q5di+bmZuzduxd33XUXPv30U9x2222xlkYIOcr561//inPOOQdz587Ft771LTQ2No74mq6uLqxevRpLlizB/Pnz8Z3vfAe7du0ynLNnzx7ceeedOOOMM7B06VI89NBD6OnpsbRukULjiBAHufPOO/Hqq69i1qxZmDt3Lr766it8+OGHWLJkSaylEUIcQJUkqJLswCuy1b9fffVVXHnllTjvvPPw6KOPYs+ePViwYAEOHz48omu+8Y1voK+vD/fffz9WrVqFxsZGnHrqqdrCt+3t7Vi2bBkKCwuxevVqrFy5Ei+88AIuuOCCmK5DxYBsQgghxGb8Adktlf8Ld0aG/eV1dSFv8glhB2RPmTIFZ599Np566inv9Z2dGDt2LJ544gl8+9vfjvqavr4+JCUlade0t7cjOzsbb7zxBi655BJtJqZ+C6VNmzbh9NNPx9atWzFjxoyo22Ak0HNECCGEHMU0NDSgsrIS5513npbmdrsxf/58vP/++yO6Rm8YAcBbb72F5ORkzJo1C4B3eYbAvSX972PpOWJANiGEEDJK6ezsNLxPTk4Omu1aX18PACgoKDCkFxQUoLq62jTfSK55++23ceedd6KtrQ39/f1Yt24dysrKTPNVVRU/+clPMHXqVMOMX6eh54gQQghxCoe3DykqKkJmZqb2Wr16dZAk/8zaQC9PcnIy+vv7TasRyTWnnnoqXn75Zfz5z3/G6aefjmuvvTZksPfdd9+NDRs2YM2aNXC5XGE0qD3Qc0QIIYSMUurr6w0xR2ZrpOXm5gIAWltbDemtra3Iy8szzTeSa/yG2YwZM3DmmWeiuLgYv/vd7/DjH//YcN4DDzyA3/zmN3j77bcxe/bs8CpoE/QcEUIIIaMUt9tteJkZR+Xl5cjMzMRnn32mpamqis8++wxz5swxzTeaawBvPFFmZiY6OjoM6T/+8Y/x+OOP46233sLpp58eaTUth8YRIYQQ4hSS5NwrTBISEnDjjTfi6aefRkNDAwDgqaeeQktLC66//nrtvNtvvx3XXntt2Nc0Nzfj4YcfxpEjRwB4A6yfeeYZ7Ny5ExdeeKGW76pVq/Doo4/irbfewhlnnDGS1rUMDqsRQgghRzkPPfQQ9u3bh9LSUmRnZ2NgYAAvvfQSysvLtXPq6urQ1NQU9jXZ2dno6enBscce691XrrUVubm5eP7557Fo0SIA3gUg77//fmRnZ2PFihUGTU888QSWLl3qQO2D4TpHhBBCiM1o6xxVb3FunaPymRFvPNva2oqDBw9iwoQJSExMNHxWX1+PgYEBlJaWhn0N4PUY1dXVwe12Iycnx/BZX18fKisrTbUUFxfHbNNcGkeEEEKIzYhiHBEvjDkihBBCCNFB44gQQgghRAeNI0IIIYQQHZytRgghhDiFbvVq28shUcPWI4QQQgjRQeOIEEIIIUQHjSNCCCGEEB2MOSJkFDAwMIDu7m5kZWUBAHp7e033UCKExBZVkqE6EA/kRBmjGbYeIaOADz74ANnZ2XjyyScxfvx4pKenY+rUqfj0009jLY0QQoSDxhEho4g1a9bg888/R2dnJ5YuXYqLL74Yhw4dirUsQggRChpHhIwiHn30URQWFiI1NRWPPPII+vr68Morr8RaFiGECAVjjggZRcyePVv7OyUlBdOmTcPOnTtjJ4gQYkSSAZnrHMU7bD1CRhEej8fwfmBgAAkJ/B+IEEIigcYRIaOITz75RPu7o6MD27dvx4wZM2KoiBBCxIPGESGjiNtuuw2ffPIJqqqqcOONNyI/Px+XXXZZrGURQvz4tw9x4kWihq1HyChi9erVuOOOO7BgwQJ0d3fjf/7nf5CYmBhrWYQQIhQMRiBkFHHJJZfgkksuibUMQggRGnqOCCGEEEJ00HNEyCggMTERmZmZsZZBCBkOp+KBGHM0Ith6hIwCzjzzTLS3t8daBiGEjApoHBFCCCGE6OCwGiGEEOIUHFYTArYeIYQQQogOGkeEEEIIITpoHBFCCCGE6GDMESGEEOIQqiRBdSAeSJUk28sYzdBzRAghhBCig8YRIYQQQogODqsRQgghTsGp/ELA1iOEEEII0UHjiBBCCCFEB40jQgghhBAdNI4IIYQQQnTQOCKEEEII0UHjiBBCCCFEB6fyE0IIIU4hSd6XE+WQqKHniBBCCCFEB40jQgghhBAdNI4IIYQQQnQw5ogQQghxCm4fIgRsPUIIIYQQHTSOCCGEEEJ0cFiNEEIIcQhVkqE6MOTlRBmjGbYeIYQQQogOeo4IIYQQAo/Hg08++QQtLS2YPXs2JkyYYMk1Vp3jJPQcEUIIIUc5zc3NOPHEE3HNNdfg6aefxnHHHYfVq1eP+BqrznEaeo4IIYQQp4jTqfy33347XC4XduzYgdTUVLz55pu44IILsHTpUsydOzfqa6w6x2noOSKEEEKOYo4cOYLXX38d3/72t5GamgoAWL58OSZPnowXX3wx6musOicW0HNECCGEOERnZ6ej5QSWl5ycjOTkZENaVVUVent7MWPGDEP68ccfj61bt5rmH841Vp0TC2gcEUIIITaTlJSEcePGYdLkyY6VmZ6ejqKiIkPaAw88gAcffNCQ1tHRAQDIyckxpOfm5mLPnj2meYdzjVXnxAIaR4QQQojNpKSkYPfu3ejr63OsTFVVIUmSIS3Qa6RP6+7uNqR3d3cjJSXFNO9wrrHqnFhA44gQQghxgJSUlJj+4IeirKwMAFBXV2cIgK6trdU+i+Yaq86JBQzIJoQQQo5icnNzcfLJJ+O1117T0urq6vDpp5/i/PPP19I+/vhjvPfee2FfY9U5sUBSVVWNWemEEEIIiTkbN27E4sWLcd1112HmzJn47W9/i7y8PKxfvx4ulwsAcPnll6OpqQkbN24M+xqrznEaeo4IIYSQo5z58+fjiy++QHp6Oj7//HN861vfwjvvvGMwTubPn48lS5ZEfI0V5zgNPUeEEEIIITroOSKEEEII0UHjiBBCCCFEB40jQgghhBAdNI4IIYQQQnTQOCKEEEII0UHjiBBCCCFEB40jQgghhBAdNI4IIYQQQnTQOCKEEEII0UHjiBBCCCFEB40jQgghhBAdNI4IIYQQQnT8f3SvkDuFijWQAAAAAElFTkSuQmCC" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "execution_count": 3 + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": "## 4. Appendix", + "id": "5da58ff50aba3b12" + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": "### 4.1. Heisenberg Uncertainty Principle", + "id": "51f5d5d24cf550f3" + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}